###### Av(1432, 2143)
Counting Sequence
1, 1, 2, 6, 22, 89, 381, 1696, 7781, 36572, 175277, 853410, 4209376, 20988122, 105611537, ...
Implicit Equation for the Generating Function
$$\displaystyle x \left(x -1\right) \left(16 x^{8}-92 x^{7}+228 x^{6}-343 x^{5}+345 x^{4}-222 x^{3}+100 x^{2}-27 x +3\right) \left(2 x -1\right)^{2} F \left(x \right)^{8}-\left(32 x^{12}-320 x^{11}+1432 x^{10}-3852 x^{9}+7040 x^{8}-9269 x^{7}+8950 x^{6}-6305 x^{5}+3206 x^{4}-1111 x^{3}+197 x^{2}-x -3\right) \left(2 x -1\right)^{2} F \left(x \right)^{7}+\left(2 x -1\right) \left(32 x^{15}-432 x^{14}+2768 x^{13}-11136 x^{12}+31286 x^{11}-64773 x^{10}+101885 x^{9}-123424 x^{8}+115026 x^{7}-81514 x^{6}+42660 x^{5}-14927 x^{4}+2235 x^{3}+556 x^{2}-288 x +34\right) F \left(x \right)^{6}-\left(2 x -1\right) \left(64 x^{15}-880 x^{14}+5584 x^{13}-21768 x^{12}+58508 x^{11}-115027 x^{10}+170159 x^{9}-190187 x^{8}+157491 x^{7}-90705 x^{6}+27461 x^{5}+7657 x^{4}-14059 x^{3}+7275 x^{2}-1748 x +162\right) F \left(x \right)^{5}+\left(16 x^{17}-176 x^{16}+728 x^{15}-816 x^{14}-4623 x^{13}+24411 x^{12}-57292 x^{11}+71304 x^{10}-12983 x^{9}-134003 x^{8}+305614 x^{7}-403001 x^{6}+374932 x^{5}-251513 x^{4}+116646 x^{3}-34673 x^{2}+5843 x -420\right) F \left(x \right)^{4}+\left(-80 x^{15}+1128 x^{14}-7732 x^{13}+34582 x^{12}-113186 x^{11}+284672 x^{10}-560167 x^{9}+869521 x^{8}-1074044 x^{7}+1061462 x^{6}-829369 x^{5}+492560 x^{4}-208617 x^{3}+57889 x^{2}-9257 x +639\right) F \left(x \right)^{3}+\left(x -1\right) \left(8 x^{15}-88 x^{14}+382 x^{13}-216 x^{12}-6245 x^{11}+37395 x^{10}-120348 x^{9}+260401 x^{8}-411296 x^{7}+494948 x^{6}-457144 x^{5}+313396 x^{4}-149465 x^{3}+45555 x^{2}-7826 x +570\right) F \left(x \right)^{2}-\left(x -1\right) \left(44 x^{13}-384 x^{12}+1001 x^{11}+1486 x^{10}-17219 x^{9}+57506 x^{8}-119599 x^{7}+176555 x^{6}-188454 x^{5}+141157 x^{4}-70504 x^{3}+21931 x^{2}-3792 x +276\right) F \! \left(x \right)+\left(x^{13}-3 x^{12}-17 x^{11}+99 x^{10}-163 x^{9}-195 x^{8}+2101 x^{7}-7043 x^{6}+13253 x^{5}-14693 x^{4}+9594 x^{3}-3586 x^{2}+704 x -56\right) \left(x -1\right)^{2} = 0$$
Recurrence
$$\displaystyle a \! \left(0\right) = 1$$
$$\displaystyle a \! \left(1\right) = 1$$
$$\displaystyle a \! \left(2\right) = 2$$
$$\displaystyle a \! \left(3\right) = 6$$
$$\displaystyle a \! \left(4\right) = 22$$
$$\displaystyle a \! \left(5\right) = 89$$
$$\displaystyle a \! \left(6\right) = 381$$
$$\displaystyle a \! \left(7\right) = 1696$$
$$\displaystyle a \! \left(8\right) = 7781$$
$$\displaystyle a \! \left(9\right) = 36572$$
$$\displaystyle a \! \left(10\right) = 175277$$
$$\displaystyle a \! \left(11\right) = 853410$$
$$\displaystyle a \! \left(12\right) = 4209376$$
$$\displaystyle a \! \left(13\right) = 20988122$$
$$\displaystyle a \! \left(14\right) = 105611537$$
$$\displaystyle a \! \left(15\right) = 535638107$$
$$\displaystyle a \! \left(16\right) = 2735303546$$
$$\displaystyle a \! \left(17\right) = 14052318081$$
$$\displaystyle a \! \left(18\right) = 72576606964$$
$$\displaystyle a \! \left(19\right) = 376616279797$$
$$\displaystyle a \! \left(20\right) = 1962646712114$$
$$\displaystyle a \! \left(21\right) = 10267016702607$$
$$\displaystyle a \! \left(22\right) = 53895142688122$$
$$\displaystyle a \! \left(23\right) = 283807158368210$$
$$\displaystyle a \! \left(24\right) = 1498814755776705$$
$$\displaystyle a \! \left(25\right) = 7936344718181112$$
$$\displaystyle a \! \left(26\right) = 42126008006042152$$
$$\displaystyle a \! \left(27\right) = 224107780692072667$$
$$\displaystyle a \! \left(28\right) = 1194727534919520715$$
$$\displaystyle a \! \left(29\right) = 6381491115295466765$$
$$\displaystyle a \! \left(30\right) = 34147539809674959051$$
$$\displaystyle a \! \left(31\right) = 183032793143464260058$$
$$\displaystyle a \! \left(32\right) = 982616083490440149184$$
$$\displaystyle a \! \left(33\right) = 5283015487751599026270$$
$$\displaystyle a \! \left(34\right) = 28443586396635718275494$$
$$\displaystyle a \! \left(35\right) = 153340211415040987386363$$
$$\displaystyle a \! \left(36\right) = 827684383873305999315780$$
$$\displaystyle a \! \left(37\right) = 4472814607156698124909148$$
$$\displaystyle a \! \left(38\right) = 24197877589473740641311162$$
$$\displaystyle a \! \left(39\right) = 131047527967041143291732804$$
$$\displaystyle a \! \left(40\right) = 710415487340274404130193623$$
$$\displaystyle a \! \left(41\right) = 3854842259859593204491614768$$
$$\displaystyle a \! \left(42\right) = 20935895118297109855038307220$$
$$\displaystyle a \! \left(43\right) = 113801693708552958584926065319$$
$$\displaystyle a \! \left(44\right) = 619100283073677586145586922079$$
$$\displaystyle a \! \left(45\right) = 3370639793619142838758248697188$$
$$\displaystyle a \! \left(46\right) = 18364867053635351493198268875970$$
$$\displaystyle a \! \left(47\right) = 100132105010369981284602913597540$$
$$\displaystyle a \! \left(48\right) = 546331084709183792155611409438031$$
$$\displaystyle a \! \left(49\right) = 2982793537106174605376607710774808$$
$$\displaystyle a \! \left(50\right) = 16295348349815214138786686342645103$$
$$\displaystyle a \! \left(51\right) = 89077172384856173767081316201763168$$
$$\displaystyle a \! \left(52\right) = 487215721429608735330476910622825553$$
$$\displaystyle a \! \left(53\right) = 2666359028244640150695105857388293743$$
$$\displaystyle a \! \left(54\right) = 14599881495993745183130163964303045587$$
$$\displaystyle a \! \left(55\right) = 79984311982165625120087302076410582256$$
$$\displaystyle a \! \left(56\right) = 438406465556000009070524667032607361607$$
$$\displaystyle a \! \left(57\right) = 2404130564166785834625721730151135619712$$
$$\displaystyle a \! \left(58\right) = 13189879312881735090352204706269500459731$$
$$\displaystyle a \! \left(59\right) = 72396630207050558211832173949329416470149$$
$$\displaystyle a \! \left(60\right) = 397542967348089315951547292392578121588062$$
$$\displaystyle a \! \left(61\right) = 2183894994041059915175987113553259874162482$$
$$\displaystyle a \! \left(62\right) = 12002050554084516116966799647490008474323520$$
$$\displaystyle a \! \left(63\right) = 65985653791240643463075981407847701538565219$$
$$\displaystyle a \! \left(64\right) = 362918067466629583013198126157006623893015717$$
$$\displaystyle a \! \left(65\right) = 1996767590190158393756462112331881086669224955$$
$$\displaystyle a \! \left(66\right) = 10990094287514771742179326190774845175683521452$$
$$\displaystyle a \! \left(67\right) = 60509785779853871477773677060148777540777077328$$
$$\displaystyle a \! \left(68\right) = 333269558224862374477003577692960443473791291610$$
$$\displaystyle a \! \left(69\right) = 1836146128371920350494379692136256882578614367768$$
$$\displaystyle a \! \left(70\right) = 10119436236675113553217791917883221941207393477599$$
$$\displaystyle a \! \left(71\right) = 55787765578044268896384454021418899568821793245347$$
$$\displaystyle a \! \left(72\right) = 307646120979237594947764148658307876199628995135430$$
$$\displaystyle a \! \left(73\right) = 1697032491117414542044324457220996903749083983860688$$
$$\displaystyle a \! \left(74\right) = 9363790011483067005420205189409817401368646093620142$$
$$\displaystyle a \! \left(75\right) = 51681209055482287783875629020780525861732941558547866$$
$$\displaystyle a \! \left(76\right) = 285318533542305760727343900670887236876191494512992198$$
$$\displaystyle a \! \left(77\right) = 1575580409501868531852776092597622066921537055742498425$$
$$\displaystyle a \! \left(78\right) = 8702850094413415999079549099395945379902565096734995437$$
$$\displaystyle a \! \left(79\right) = 48082823044038029469169860432921834316457747753051751587$$
$$\displaystyle a \! \left(80\right) = 265719377963952146712552172789649152577423146752355129463$$
$$\displaystyle a \! \left(81\right) = 1468786596041221898929834958590410003069679639250165892369$$
$$\displaystyle a \! \left(82\right) = 8120707450830872376756191550788358119254709201587095511272$$
$$\displaystyle a \! \left(83\right) = 44908267373363930590751997156269760352323615613452654753802$$
$$\displaystyle a \! \left(84\right) = 248401188437134467754627542124649905782276108322904545928414$$
$$\displaystyle a \! \left(85\right) = 1374275242807331688425231420014324419239992603718982482559661$$
$$\displaystyle a \! \left(86\right) = 7604738557552716156580386424231742733114905755171433445549224$$
$$\displaystyle a \! \left(87\right) = 42090420857263381192531874532216384034537636743943430610191814$$
$$\displaystyle a \! \left(88\right) = 233006823103906644200422880459226361845439242282843171642669023$$
$$\displaystyle a \! \left(89\right) = 1290144761215931080911710396066664958430549907023572193651477537$$
$$\displaystyle a \! \left(90\right) = 7144811770968667481378014545656873893259384913409655144496012778$$
$$\displaystyle a \! \left(91\right) = 39575267311948353143765940720152956383039278193579416928245990030$$
$$\displaystyle a \! \left(92\right) = 219248116518653719463970863675403515896542627397438621423247676150$$
$$\displaystyle a \! \left(93\right) = 1214856899184842110869818154421260253518695343807743774412141659924$$
$$\displaystyle a \! \left(94\right) = 6732710824119213048804962757939819797158387602018712615957143394929$$
$$\displaystyle a \! \left(95\right) = 37318895363880911059341062056247102009426734591812596507859219303078$$
$$\displaystyle a \! \left(96\right) = 206890251871266564392965813834320082452099327112961556537078851602575$$
$$\displaystyle a \! \left(97\right) = 1147155263872001466637467068758034565047657963495811554659031657665516$$
$$\displaystyle a \! \left(98\right) = 6361709661594123891322707742514525826881467071012100180838455919140343$$
$$\displaystyle a \! \left(99\right) = 35285277943880850411448155851666068051580373694247142796564645617354951$$
$$\displaystyle a \! \left(100\right) = 195740154230696177131521702567160635847499234135843856951110163064946553$$
$$\displaystyle a \! \left(101\right) = 1086004602452197031766496315055195255739423382904725050816006732107437542$$
$$\displaystyle a \! \left(102\right) = 6026254539927397710876889540349534659377957014082703206645607781428292920$$
$$\displaystyle a \! \left(103\right) = 33444606595778477923661328202122649514186933679068860811874939116272515697$$
$$\displaystyle a \! \left(104\right) = 185637756158580363376931227547585262125239212875670550798078988061866677434$$
$$\displaystyle a \! \left(105\right) = 1030544967204484480053157098934603074993420981899397824335782181625882700380$$
$$\displaystyle a \! \left(106\right) = 5721723325654802340937834126672966051608620389569118423133134003192206885382$$
$$\displaystyle a \! \left(107\right) = 31772026520980077776251454260288376866497468059991184550330366578808668683008$$
$$\displaystyle a \! \left(108\right) = 176449345333473913476095864182102820753709279105933343149823461827035366603540$$
$$\displaystyle a \! \left(109\right) = 980056706656382785258588573502216824589033603590747570762502413451423599638567$$
$$\displaystyle a \! \left(110\right) = 5444241132838660120038836666730879719193718474282484003830044314163719842951165$$
$$\displaystyle a \! \left(111\right) = 30246665051918541010293783185489423469275634132317905609799260295584262769297211$$
$$\displaystyle a \! \left(112\right) = 168062441618914035120909132690830354100328803481897630550093553615523914310881691$$
$$\displaystyle a \! \left(113\right) = 933933434797555015316040931506278351692789526980516965743449138076620454699199453$$
$$\displaystyle a \! \left(114\right) = 5190537608097484430642409330446482045368682008392854653202108918307747617534679982$$
$$\displaystyle a \! \left(115\right) = 28850877696267022668285262892133793024136504892644798318365583191248959670486512608$$
$$\displaystyle a \! \left(116\right) = 160381811565295775248624296455866421716714346991289154493397789121750374393404105246$$
$$\displaystyle a \! \left(117\right) = 891660950878262235347802315382425648152892813662053079298412292144629709770632807591$$
$$\displaystyle a \! \left(118\right) = 4957835368294306580691330860719269629203499036444258059905858256163645404952691963068$$
$$\displaystyle a \! \left(119\right) = 27569657383634636490158975010289460553771314109690952688533114282176131344827591452931$$
$$\displaystyle a \! \left(120\right) = 153326338468757919026339581008993374955014479963889496434629975009435436180210357058053$$
$$\displaystyle a \! \left(121\right) = 852800647242884070383122314412913804739947580709846904289007507382442166589338378015366$$
$$\displaystyle a \! \left(122\right) = 4743761996490637323784959981968575655680727079967536196841572595001377583777770027718877$$
$$\displaystyle a \! \left(123\right) = 26390167450809626861998288496507198823002020347384895653610609571240704149361658077326520$$
$$\displaystyle a \! \left(124\right) = 146826542763862942947104914842278231586905721283224782950160046863373175363406298202590942$$
$$\displaystyle a \! \left(125\right) = 816976337212691360153524715237575047130836978370349729524712302055405417813559674915795194$$
$$\displaystyle a \! \left(126\right) = 4546280034414061215933315778920318830713899608114165172836174785597604586382199482880974708$$
$$\displaystyle a \! \left(127\right) = 25301369381484079421369786935826121343988269578112395716912549269463944544173284409145267510$$
$$\displaystyle a \! \left(128\right) = 140822601601823333865392381928362104632672614861501079465347882168354019519217244891280557010$$
$$\displaystyle a \! \left(129\right) = 783863714270810312908727021652100595963451035647138647097301549963081967106707056346312257158$$
$$\displaystyle a \! \left(130\right) = 4363630852759252407841550460249638288376855087262413611308424362407537880015959549708477385609$$
$$\displaystyle a \! \left(131\right) = 24293723779627851753942222039231093608685075534786585515576697435029136114856314048222914714247$$
$$\displaystyle a \! \left(132\right) = 135262755092688034312927407679306138611025951789209200577455341026161385089251279061199268995441$$
$$\displaystyle a \! \left(133\right) = 753181853863432947690685973774243677253584658377125009657141417578825101333703803370121386054840$$
$$\displaystyle a \! \left(134\right) = 4194289317568913091492621598303931371001786841778941073800242267107915669957964422096673382864762$$
$$\displaystyle a \! \left(135\right) = 23358948433891641893113761480249731920552344330698625226739905031097953944109802114250466040259645$$
$$\displaystyle a \! \left(136\right) = 130102014604224477853558788658710870484639046296257670053455881404072582155074325008793938082575127$$
$$\displaystyle a \! \left(137\right) = 724686314112097189888106547082032257856520755334928905740609461422812287262147936039373544508413883$$
$$\displaystyle a \! \left(138\right) = 4036926924440565990740883979138256258834610867158674805104800339310681742753803395235098561429772609$$
$$\displaystyle a \! \left(139\right) = 22489821249099404969649848944966276512804301439609492080996639844023788842824926464457416234950342464$$
$$\displaystyle a \! \left(140\right) = 125301108903009833648529090020199353788840777325426923229792595258634924119978581959895025727522986413$$
$$\displaystyle a \! \left(141\right) = 698163497922934316719570578608388819916246441571685095088570508418135496445621157437588139375609855493$$
$$\displaystyle a \! \left(142\right) = 3890381625617281340589809081419341310506830523546592649590703889385413582804014963998912572033230543708$$
$$\displaystyle a \! \left(143\right) = 21680018705709481934561602114917125773607272962192415331603381382197384416323868708350020928052980317485$$
$$\displaystyle a \! \left(144\right) = 120825618972981865945585967342182936424042290550526403191891650315379238426661969725285199267676974015565$$
$$\displaystyle a \! \left(145\right) = 673426017537967091880265278241845684526711952450705818965332318485994674589531623428737203442064447315288$$
$$\displaystyle a \! \left(146\right) = 3753632985336680949780047506191595380342107513923957114138590238644315511548946935957954664332044188895231$$
$$\displaystyle a \! \left(147\right) = 20923982652446800019398110482738336180891514309056658187696153887287642849394064219415446135300123168716772$$
$$\displaystyle a \! \left(148\right) = 116645263559330382937195619801420744192472042303318229641837242171521943219398445271457599684431276975666333$$
$$\displaystyle a \! \left(149\right) = 650308861236893562623911955376075658118095207148033849764719726600489178074029067062333824512339574198420587$$
$$\displaystyle a \! \left(150\right) = 3625781605901786488930297528719290281565544820439820659804195432582727382384458460828932624208424305729508435$$
$$\displaystyle a \! \left(151\right) = 20216809845719427851242884579291091708919751052266993570473895574438442069318065740092326897632605389906621459$$
$$\displaystyle a \! \left(152\right) = 112733305914311212977516956923650251412204072472594052728492014145046059700286210313699424368008152086913131376$$
$$\displaystyle a \! \left(153\right) = 628666206090642456075371864977475100028182109529722534102275124611119690922930808307430311985449429487587958732$$
$$\displaystyle a \! \left(154\right) = 3506031998766276652645998119888422118363249917382891130575026895775569031807121090320737419649617604907291947977$$
$$\displaystyle a \! \left(155\right) = 19554159866191737922814909739149772464108283797284935326609653401040670739629961459750570315732045192835090752940$$
$$\displaystyle a \! \left(156\right) = 109066058610951559600706739434172785093458905289109906419897478303580523461518754964555407464421004562171724774736$$
$$\displaystyle a \! \left(157\right) = 608368754236220007387891819328337931237795994504518059102849292105462661312871380296095659063958411895793326658388$$
$$\displaystyle a \! \left(158\right) = 3393678251371727658628058520381670239982826208523798477412538828920766989621798673749066073861901042220599712661378$$
$$\displaystyle a \! \left(159\right) = 18932177970781413427938988412853060515612388211082574987616680410953687383427533700594546440300842853979149598217994$$
$$\displaystyle a \! \left(160\right) = 105622468172571739041278014348155666727241903746060539461134952544746614882166037274126454886561887603383933556685408$$
$$\displaystyle a \! \left(161\right) = 589301495839912502144527152058477031085385583849231403974814118732124467768939710288490189065194852558667870866284764$$
$$\displaystyle a \! \left(162\right) = 3288091975802904877764457538841887204697480726250454227589596601929135652446689308131575021850492241186007645438951468$$
$$\displaystyle a \! \left(163\right) = 18347430151338393826159100475098884676321298620734587054773494327082218145060159272152438696708289951365270785561195983$$
$$\displaystyle a \! \left(164\right) = 102383765024189137091592136242897536047448812070542928976275705529635234641246087901555391172575698779801320745951505282$$
$$\displaystyle a \! \left(165\right) = 571361821733636417111944530650059310951463194341325026653830234204594612936215336317685870923213149077223847300599381067$$
$$\displaystyle a \! \left(166\right) = 3188712129877107881568395738652651622188967877034115774755380200850192034071413785494792922537535835438792311148038826707$$
$$\displaystyle a \! \left(167\right) = 17796848223061987981545173887688525318788181116894878853053271873945928157483434149998073345587131143999948793978943247766$$
$$\displaystyle a \! \left(168\right) = 99333167185408583883944637657209363812153779285952459316746511483069461295264435525627729556297227115579525770014732648967$$
$$\displaystyle a \! \left(169\right) = 554457924099377992146163166619478435145662543617870017315894738869301383583938512999063013110473901672283383183568242098887$$
$$\displaystyle a \! \left(170\right) = 3095036382612332215800973866709490769642459399638200854677748827547737839555746742256841664692585694221567710640045221185872$$
$$\displaystyle a \! \left(171\right) = 17277683195666686899414398775436951083624184566096345869560277689488465943220115750242838953181245313213546087405292753937206$$
$$\displaystyle a \! \left(172\right) = 96455628398322253671244029266221858647446750208838416046429202993754593554793048569182973647220217918084291504154809901721433$$
$$\displaystyle a \! \left(173\right) = 538507435607613772186142918239743248678607349357347876053221538100539146783913053360199287171551719210654551557086321503782975$$
$$\displaystyle a \! \left(174\right) = 3006613759697814703889674260444861961187020502263501191731453543352008000930174429648715779609937149184102894117628485417910074$$
$$\displaystyle a \! \left(175\right) = 16787465517484055267193303611068473212400403792634393651328496429238032241247795040119561790156528151648024153447044386116973435$$
$$\displaystyle a \! \left(176\right) = 93737623169962239450375334362460106663975979779834337084994949367985945561328452324359972167590272959831357763096577054118313749$$
$$\displaystyle a \! \left(177\right) = 523436266879686825613766973007990243557227029701807927615076568541736361009320264638437349727151467974631396337788926884461872992$$
$$\displaystyle a \! \left(178\right) = 2923038354759171567431235365787547983309639785426184415499560799314184712591855867112103390284816352844983264778203737966969917775$$
$$\displaystyle a \! \left(179\right) = 16323971048727331777788733120548627496321937174685125729131787305772584164632510237851092745198943149473572003597351505582386319557$$
$$\displaystyle a \! \left(180\right) = 91166962620140266196380652327963800298748593031072191421829663637920557231380041302281613331941229703078223040215805833983480294499$$
$$\displaystyle a \! \left(181\right) = 509177609633448477837306828705609800362836740354048597137859683574934641556448620051568432588276967385053690183418116323280645137278$$
$$\displaystyle a \! \left(182\right) = 2843943931968253419735010479238980295033109133668823986994415540150428193464944905169776250658480490631606796850260963777340351994618$$
$$\displaystyle a \! \left(183\right) = 15885191831278212189857354016234389223083175302277668716503103108664761400577864874751512750646588095309014912783163951052405205240595$$
$$\displaystyle a \! \left(184\right) = 88732636147109070846890790754516014393899600901834415781086374677548086912443286146739455717046443682568003155896865687861723188669609$$
$$\displaystyle a \! \left(185\right) = 495671078831780313304851726400122621336617810500320344604569875322039239064880842824204384000618772663067659498030026594975009908747293$$
$$\displaystyle a \! \left(186\right) = 2768999277232233545714454481827760889946432960123776835955534165217519738345767218834910041332306895352183747412920004084758161108320993$$
$$\displaystyle a \! \left(187\right) = 15469310890842522960599915746210719682945678758630817795286982915584431369488124379706895110767852757450251663297223355104267228740085772$$
$$\displaystyle a \! \left(188\right) = 86424674819735039896799118861310661928864912413163518203563613249092646397578813532694226276085304999311713805290257319525893816454703829$$
$$\displaystyle a \! \left(189\right) = 482861971922723712462447349906719331633162427531250728763701875008431601814611128038672674766571227753712801614671401865314826612911160525$$
$$\displaystyle a \! \left(190\right) = 2697904180581797937148280581543296551798708945370665582865245964381716687828326176106685592655591793011515799246698061666345711883762091012$$
$$\displaystyle a \! \left(191\right) = 15074680442487308589014136753849400037083968218506312413016156167129850552808978686421969887297698349297390008904048162812419702673015032050$$
$$\displaystyle a \! \left(192\right) = 84234033124796287360994715143092397740022246931098538944313056151266637729003755006757838788186155422200131485926083742677685374268223312096$$
$$\displaystyle a \! \left(193\right) = 470700627095621359035043763953369459963625925289833974046395242804598266455740488198197394434074866751699417255622517818642335428027296919398$$
$$\displaystyle a \! \left(194\right) = 2630385952820637970914201682565772871021718533735777876742124673692267099734727008439699267226272021996388616577853511790702068530140269125164$$
$$\displaystyle a \! \left(195\right) = 14699802979552831874232764228182415461486761001079851068034594966995795034819319471713163394975999759222751576442527985351943982146733065521765$$
$$\displaystyle a \! \left(196\right) = 82152486279187832921256564856896710959591297131767272755903263052018383446722231871235229991094142350361533658436382974433313191711385560569324$$
$$\displaystyle a \! \left(197\right) = 459141865577811629864464723080839529767224393761592554178295858028222665885938866476740496261577486512550890406949077299223622618257259365578414$$
$$\displaystyle a \! \left(198\right) = 2566196396040437930308448925384608625203221944806746030150168521813221544939929998366383224972135431841204354611612429599357152842302936484884188$$
$$\displaystyle a \! \left(199\right) = 14343314814224876758823185160086176786474515954256795099147137717782196074013983887687462343977473494605369894613643743993253790694165144695262384$$
$$\displaystyle a \! \left(200\right) = 80172540788203522350461148875475983469714450244904615838562877676793108502193480905452084173691145111099268038150992460412926031426483798219677784$$
$$\displaystyle a \! \left(201\right) = 448144505513858895568196468889840234275336222947452048665769923808602850111892661771184819620309194197199508530254608089672537472469541247946343107$$
$$\displaystyle a \! \left(202\right) = 2505109161053696139375001364908344336943871698321061375015949349461874601023065247691680946255573621304401290308002230973178232876114335350144972361$$
$$\displaystyle a \! \left(203\right) = 14003971709912543591325655292639897461121148862806626993881701490617285221096284143406102597883866088998301973756385544377417158537651661034677863353$$
$$\displaystyle a \! \left(204\right) = 78287356315150712421345570599291459236151221630895951265869061887608419927458971093081059364670096829178249046870162310052143476639411849664880416540$$
$$\displaystyle a \! \left(205\right) = 437670937022779842842943234134206616799253799749581951012742688740352015559569518297583255569541442833797892441352766142258530818667109896948485754084$$
$$\displaystyle a \! \left(n +206\right) = \frac{524288 \left(308100594085461799471252811929015395268676981815146993478897765626368 n^{7}+118257238845329534104166647459207205826160815534702066927201691345265088 n^{6}+19452382884104988692303022435475135901842909178290152010319499964414470992 n^{5}+1777586435645022546351259041138820323602003786267861298885267380026031803740 n^{4}+97459452721184294360421516929908757666354958852802805051265008541617435502212 n^{3}+3205909734821573376664306285269678308833771565004941858959788300378219143414967 n^{2}+58585175155759444283503073167103938801944011798643915253626834733273868772094623 n +458804687018609308592231375916505063933880270638902326033434479266392594410358290\right) a \! \left(n +55\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{524288 \left(670219198584436658134511583493843674473168911704512135702288739046784 n^{7}+261914505584810481754576989192015400494064325427594620246977462294264512 n^{6}+43864032922057380255228052544143915624055960003207564030466298935704134316 n^{5}+4081004449579274195021500565336162463499685844165356528602487055422209966860 n^{4}+227802123501128745112329565509289977286069822998862348894945819148020578652691 n^{3}+7629210916265562201857267259843330272595401200394272773033524218107441506301738 n^{2}+141941001980889811764888862655603038465783600901660354099555935305512116003212999 n +1131715456581836609748494072063783587895532677940050206428269104670902624904784600\right) a \! \left(n +56\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{262144 \left(2844876665924896085327464959338483488314515883308536241952218163006928 n^{7}+1131454160523455286737419809968419964410764653402659196595998045895438384 n^{6}+192847552000893491176216090742437962477778337963504641738659366529951268704 n^{5}+18259896598875558597412152111343863479824766229073139731932910450418032704540 n^{4}+1037319128009165248289617355588927830064348518952498660124610597453879653624457 n^{3}+35355378359502257429213431005751444002941610067211724880110300833639822372568501 n^{2}+669426706673281378868982866891447533523636569336574592064259874238652318638380606 n +5431877088578836126842372394908436583653416807568628227589865065077974341502831390\right) a \! \left(n +57\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(193246323075514832514366463632134462526005208529097744285610636632375618689607776 n^{7}+117992368696395758431188144637523018572275988337838804103670995650239754823771022856 n^{6}+30872644666024613600710797948525297430837412265323936172438267123533789905047968150158 n^{5}+4487191860903440114755083707015977979068584657062037381087773912226563927593211836095075 n^{4}+391272609525210788736102525607028338390096700326858313355068181978536053434334177554255394 n^{3}+20468574340676827185221338286310858090910527386848090533439696656382405199592444589775767509 n^{2}+594805046886268894910413190079767062392232393905564081061863341102416699418066448624371418252 n +7406885212649298273474748580275654711980404928858089288039395926991923024383901552922797699180\right) a \! \left(n +89\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(22449018171892670362741993799146767858673093361752547092254737810235898321149664 n^{7}+12540532194620477308053437603147296104470902016289539421500298419235187774830552864 n^{6}+3002130787471641397377384623621258995604021752318526729526250825763130372696209645056 n^{5}+399247566845474296340180699700042025860544829303961562179397040684022876417888585852720 n^{4}+31854988272568626915351657986156805383552156235417026590021197570781984274290442778230926 n^{3}+1524877067976975234438161871629574294936938113688084169890912399042547412744707932512127151 n^{2}+40549955103024810066433502651390566535054022958127844143651137798910632623367654670472262989 n +462103757086493465142328066397349523429774310354068072336192037163837409511366862559732862340\right) a \! \left(n +81\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(46773762727471688456 n^{5}+46352743924342950713128 n^{4}+18374058849450245042620015 n^{3}+3641675926440583003797828509 n^{2}+360881013266475945164403692412 n +14304850185116048426862157694880\right) a \! \left(n +201\right)}{5395222944 \left(n +203\right) \left(n +204\right) \left(n +205\right) \left(n +206\right) \left(n +207\right)}+\frac{33849922949209616891772928 \left(2 n +3\right) \left(395412976 n^{6}+7345066704 n^{5}+55340929120 n^{4}+215143330800 n^{3}+450919294369 n^{2}+475583621391 n +191328405450\right) a \! \left(n +3\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(8302319913582670993133101243414294184573813235162085934639293923292157621308880 n^{7}+4692053466313362107904476008575839549327725155910319890611644532676843837893820992 n^{6}+1136368653536745723566598863559552949674947764194718897029158558238103587978248735560 n^{5}+152887612228324925820850529971306032887817675679679615012111282026241036588246648983910 n^{4}+12340863034891159738389255504396444898458361656485321151613717199616050305878870913818675 n^{3}+597638554331139649421394841966559363257983892485707262795103173245579253619596041900321803 n^{2}+16077829352835368478579561315576591750022137849409553697387073770398287479681810811086083430 n +185356285649802765253064635619550292509948495859677551448445954365010470708527815348553071500\right) a \! \left(n +82\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{32768 \left(186940332326195494116573231170245315501219421359422931839994326696854432 n^{7}+78200469343931512940222957702902880439266412296672594261466271327868865664 n^{6}+14018952626532865983313270374256828316169938123281720096826128962433520288312 n^{5}+1396128582383408549971431338492468598835265674044651813428804040310295294710900 n^{4}+83418462502901184634027902200422512841496906089600367961556851540931703630104208 n^{3}+2990373153661338710128380473940475664016883075990817550639940183514131110928459471 n^{2}+59551241140840484954718992355592405542818476349586934705095137274007063210514470023 n +508222341590034161040675306305013554246811626924670352684709845306016744940213870840\right) a \! \left(n +60\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{131072 \left(11776548047501742730688235152413553009059548168161771164967009481354640 n^{7}+4764924408714862799884830963705913930045071102243158368220937630935829760 n^{6}+826220142185478403822350737943439576396776988786022203065562516573051911712 n^{5}+79586760981318114723056715159019260804386075797659474008986137647734367377960 n^{4}+4599537880988848614541595367383188050538447909048909253146606766925571394411485 n^{3}+159483288542229402005031370633839186483935730921454021857199261393135893249345505 n^{2}+3071986739325179560402519340774831994072173790668974856357459481539139636564629388 n +25358392470195156384482544603222469092315133062665619448862822691708792348774343950\right) a \! \left(n +58\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(4908518728277 n^{2}+1960503496427497 n +195760089794517354\right) a \! \left(n +204\right)}{149867304 \left(n +206\right) \left(n +207\right)}+\frac{7 \left(31335280058198664755805455315193116874916111139616349386563004635935402407559404 n^{7}+20000597226049451227092801296798921426872662344208905781027926550936230937701161064 n^{6}+5470961802801999822520741758519377667212036693033307856947234867318409720113871037139 n^{5}+831382053844640621584510699293001679030171413210405383044138103816773669146920135293315 n^{4}+75801580248248157239597504976544081800494052345507014612643373574168776501100552623729911 n^{3}+4146648260066900120636275769257196120099632305567421016758144629465149925087454251215271041 n^{2}+126018527795117868013931835764788850324868251773514561110324651305590688662833160469853814286 n +1641293733469373853509843301698578294660992629677762708406318088839845546531454214022947405480\right) a \! \left(n +93\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(91974779388246525169232904493809510883170234514952239535462991264418976724946906 n^{7}+59423108299806837208593393903113152565773076256393109845131242876923083269631799692 n^{6}+16454176577907202587048998890764176369846427083533036556470203839463456458451265155739 n^{5}+2531258816251867381149521010292120051432783238200963241180941227439530247605585684839330 n^{4}+233647692880784218684717448679920604336918523714126233944057332733217296867019079846901644 n^{3}+12940533696025066157275093465188578481116914725024594063374536674402824996318739033955883813 n^{2}+398186102929004869235638444032741763089885498336913900076941070190384599550715138878711392916 n +5251219865009152614146056673921828886111962987381323972134088221371584913041818767683374246420\right) a \! \left(n +94\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(173015179909867772611053465812108625894675670489743848954096348000774223388726820 n^{7}+106783736083451872946905050005626850252082886188573402746553220958001514848935337656 n^{6}+28242621403008792739017371922367592767208269653080363022573569361806519603186195736275 n^{5}+4149422448498622406631834885131570695384630306498041806368250831396071702960341661660535 n^{4}+365743218165668451793497869986910885319421278255956136197874924505799481735149052545928035 n^{3}+19340618135294905081001747491103298816077165389308461100516779010666247246210595407890299249 n^{2}+568127149088057075990890453962789788501723142980040112515543772037909255405871016033649448690 n +7151497773898752893484596882653308544410030229355725374651853282701152194098584795385714747240\right) a \! \left(n +90\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(75673889109487791240049893524832757461439678376628864706009921303807898334299840 n^{7}+47216801859631978259475698268378477195320290893384344038593640296965838835827062330 n^{6}+12624999770074102031299767508863466561321684777542452975626152790745290113180882601757 n^{5}+1875229766284882208469450289366215560265117709705967519999538826208548167878516455360250 n^{4}+167104969676623930947431343948433158617483198249980278898807015794195528827933935274810405 n^{3}+8933789650180954253693295158306709257706267749669483731426316708395296937965211339694281985 n^{2}+265319706496820848760796106323224837083971081204742451103188573857429825328309531564047682193 n +3376650748982084453634644153429670261540219893859231302526930028247249773101544703330677986480\right) a \! \left(n +91\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(259581391429204715126288528126265425441626014534317555380906242781140032235678332 n^{7}+163780731473270281200908693348754431742399252272767191814925602806915461352073131912 n^{6}+44283987983188930737414303778692075084944213230464256353322411135345704441470545018007 n^{5}+6651654733985887572972878786913918420037459646169278740393607745744174049996660296923820 n^{4}+599426034242286329903453751306008157000664531824463867338626806199599452344063153616522953 n^{3}+32408920054494326491909969041790487847630510474105147442151807596191793501522232390719967448 n^{2}+973403612141211160043411111772460994310220316537582059145715198548863278586240934351146063608 n +12529006926006391228323469074816974198186819292691478675151418203931518754482806038087699663440\right) a \! \left(n +92\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2166395068749415481073467392 n \left(n -2\right) \left(2 n +3\right) \left(2 n +1\right) \left(2 n -1\right) \left(2 n -3\right) \left(n +1\right) a \! \left(n \right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{18446744073709551616 \left(440823864175700194869656656 n^{7}+33768709371013457718857669424 n^{6}+1106280616637172875695028191960 n^{5}+20090725820951011283679870122280 n^{4}+218426097304448718573942462567109 n^{3}+1421572200775520859209402500967571 n^{2}+5127947526590512248513555139386360 n +7908686383939060514188686713328600\right) a \! \left(n +11\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4611686018427387904 \left(8069384870050307665408745824 n^{7}+674763002645416395300974055616 n^{6}+24138498730560697902156520472648 n^{5}+478851976114500431187774625507100 n^{4}+5688908741706147491428403173479556 n^{3}+40473933673082918798827680997825149 n^{2}+159661505211577929661347593729399357 n +269391379421132665684693863843057960\right) a \! \left(n +12\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2305843009213693952 \left(607578647403595691265534140240 n^{7}+55060084535509329673855454955056 n^{6}+2135187263383421788397844449218736 n^{5}+45929086497754957833455853512878820 n^{4}+591835334884739426969527670177774675 n^{3}+4568366671389225185308231403289364004 n^{2}+19558293095425901257548187135495716819 n +35825666243626264948917292165630789440\right) a \! \left(n +13\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(56895013138440121502541333052673195983930950861622349678410357564211133819066848 n^{7}+38272026263935429146938863043236511117549408377887144458279131243188836305439629044 n^{6}+11035277372213434746940252318905449007723039565795675007560840011838204486913971301687 n^{5}+1768008606343183128967096207089232871502814546828081726083988079949262415461092461236320 n^{4}+169984386058327924642097940006085763243918339671481007823998106085089339993021753854417677 n^{3}+9807484595302637702645570991371881916865680094513034828243580627735673568533182736289052166 n^{2}+314417563301944559370728877432334914512749592536320434443373714397834329823547006628083698708 n +4320684571474586149454281927284674843773499717561828687718845454264542664784185049600445330850\right) a \! \left(n +97\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{576460752303423488 \left(9342768763363718584614431056224 n^{7}+911947086147859188138630984907968 n^{6}+38099830047065626796704030556333144 n^{5}+883134413587555642530978065991326980 n^{4}+12265697530551778369777195432773051376 n^{3}+102072252781441303788869450639671499627 n^{2}+471236051700544471222808020986717609261 n +931044144209077588495666150030982425800\right) a \! \left(n +14\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{132226261520350065983488 \left(25041946867892048 n^{7}+1034728557876147472 n^{6}+18196807276594438856 n^{5}+176487007945682368480 n^{4}+1019152234131593356937 n^{3}+3502787842386531017143 n^{2}+6632224229546048577804 n +5334923772318768068700\right) a \! \left(n +6\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{33056565380087516495872 \left(2438894969413388656 n^{7}+118040129140878324400 n^{6}+2435936576675197781344 n^{5}+27778180148662567705060 n^{4}+189002594517106912264189 n^{3}+767118906383197820075740 n^{2}+1719390481959450143590521 n +1641404168308039071757590\right) a \! \left(n +7\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1180591620717411303424 \left(1449265659458544986896 n^{7}+80389501821425141468816 n^{6}+1903531160823886919503192 n^{5}+24938259605158738060355000 n^{4}+195198534415910529494612209 n^{3}+912703078043381499634129769 n^{2}+2360169875123135820758202618 n +2603514230467265849016748500\right) a \! \left(n +8\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{295147905179352825856 \left(108742666672728453102960 n^{7}+6799410854163184274095792 n^{6}+181636044972972592402556016 n^{5}+2686883344509078614869884460 n^{4}+23767867338876796073920954665 n^{3}+125714016280499448317803249018 n^{2}+368099925154678685068622359329 n +460251600466715109791530790040\right) a \! \left(n +9\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(4688263080817523587093249881021383482166746912863493006763740117835055330546314 n^{7}+3110021168998841007277880814996904685490213087451125840252707600829782478436706456 n^{6}+884295994276725726905250365157608159561619009567123868301204958699793932629352235838 n^{5}+139707716779929595776325227650231698860223082133684347765800247276824391829130874710880 n^{4}+13245138217519024051353235090224270138339428865470164254982202974397838773939680191076616 n^{3}+753541396069126872495159385430841251307261454358901994547142058583407431491666588069912099 n^{2}+23820432161350232423438571477227377167150167494507116947238786558690647220374034595674987822 n +322760876111128643060849399264518450502434979786914975100141458955789083867133567383363957380\right) a \! \left(n +96\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{73786976294838206464 \left(2430496857444645704845728 n^{7}+169096118198972560597438080 n^{6}+5029030090919355539531643368 n^{5}+82873621764922307363112824700 n^{4}+817185912477642714427879986752 n^{3}+4821333178973617964257567726185 n^{2}+15758058864968630081621797798727 n +22008825250341524043677705407350\right) a \! \left(n +10\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4231240368651202111471616 \left(268733956128 n^{7}+7296538433952 n^{6}+83576794712536 n^{5}+522749895344900 n^{4}+1925190031021152 n^{3}+4167586467596533 n^{2}+4901627062650674 n +2412265777785360\right) a \! \left(n +4\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{528905046081400263933952 \left(220021496307344 n^{7}+7532532874227312 n^{6}+109420744767494744 n^{5}+873667577869906200 n^{4}+4138083379554565481 n^{3}+11618510476240546563 n^{2}+17892572716308640326 n +11651468547757352580\right) a \! \left(n +5\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{57344 \left(2129118502463708262400962125248338703774269470717773515582980197776261056 n^{7}+962849573566764385432694643221759089588462244490644331667046550224998387968 n^{6}+186602782398320008319929009851561303792484983643720068131083004794751199649316 n^{5}+20090139324823221002859020678749747868891078173926242025007283153333522151352770 n^{4}+1297706613226829097273625691819403445026932104860019989140369783808554716625816789 n^{3}+50291969807922932307973061554767888287104670755659171159059113781216186199098075712 n^{2}+1082743050647060645367231692497076537223374505227779833628146603575116015181974698999 n +9989697669581854243640149724526736911739639782686229078467899393568195158015822623000\right) a \! \left(n +65\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2048 \left(100303924774798208012407507235477258348137343935958382022171783348576414720 n^{7}+46036183333655128895865891299387836314719788035002297332787809724183648421248 n^{6}+9054872842867869111399940933240027392714172543369688994995489130456839136316840 n^{5}+989398363630375517579901670886594208461433337602496548347320342554066690893835800 n^{4}+64861861762405097120485845566169891344782039248537888956972281640974980018443981170 n^{3}+2551155169524176493062575541390240038936669835689749725134899825077133226250509084547 n^{2}+55742915418882535403069653866739153080328377624444839870657425323398150836153437473355 n +521967424792031136075397826113805054173270605529187642776443340479697895783407616709240\right) a \! \left(n +66\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1024 \left(328858874550107342659355229697341233526945324510060169912001407593915736128 n^{7}+153147188730434866861241220989475037036019553115121425316032851996631749295936 n^{6}+30564038294262523167842662766550312554913087544701207441530582805741960717589728 n^{5}+3388588505703529207986811406188844775516194672263072783508308675165712858752020520 n^{4}+225401576686117890204727558195037297388597292424153867265232548786024912217583859702 n^{3}+8995492718846979755758854157556879948254260475196871920488929491446804018351847425969 n^{2}+199433895625694150835717740350859974949490228646347011444798310982914538573800803867337 n +1894848946830380401261898125262831065736919997174614401638175795045314777916390040601260\right) a \! \left(n +67\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{512 \left(1050562179570149085651590811858435112448016796328280852348343424786640285568 n^{7}+496293279373186227123801352147603342827498669497920418525303266208485334624640 n^{6}+100474950256899848395981423851480341134554694455922455736732218092484892770373624 n^{5}+11300148349910199146039376121292357978441325962449818767972995466041287898258285380 n^{4}+762502149132733069519757568910010611261405491792878050976525038918710348405582218362 n^{3}+30869419986720079121588320126223232599429221914823075640498336725065486369573946701735 n^{2}+694260523615459729675570599400140136019886084045640634503531746993778702109393116230081 n +6691426151269899532188059907162153474305399724999062837749964300865069466754122713122520\right) a \! \left(n +68\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1792 \left(467171532398131020810483260786538565684303855747071209721299360205653078304 n^{7}+223827090866605436217011305418395028016208404257576721505899636058897097996128 n^{6}+45957050678734922245659901626514166652339207034455687049360390047981711504460968 n^{5}+5242024517532057463959420290930207118294538629480081132300887568222014799439271260 n^{4}+358737682742826502650107995843744089703281702264826466327384078282263860294951267396 n^{3}+14729428660559822146466026356062486764871024368670424962042760897143561602169074890457 n^{2}+335971084652354572295058505603798925078314743932248994208910689553204326803187722656437 n +3284132119209347203668224447092998263851246167557235015739890318937361404796528082912240\right) a \! \left(n +69\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1792 \left(708529914650262645170020687309479283844197404346634840597993366988429487376 n^{7}+344206946523086137023986157241617191112282233861583910629104121417964007749280 n^{6}+71661290918400115609597536869274581380924455620593002362583495631996115445366392 n^{5}+8288145512408903419072190377929235049060512792120306880180952331688036624702454200 n^{4}+575124027728660465056741224231083366909668465380488285492355350822145402891587222009 n^{3}+23944014597520536642058123133849628187930734394857706499640086205019727932412021183150 n^{2}+553783342935881746606007614446581349677432748948184404284339830207379726532680264867253 n +5488907345722317159532365943604858979084665750470420127792634076130448618710476854485310\right) a \! \left(n +70\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{128 \left(14660302363382869193432159172302374718950560284656452932520478875969352282752 n^{7}+7220009395043471602799916348613362199169135637899793475786869214310539150299392 n^{6}+1523829440859381335253345680929893034733365317227168772387551343306524788360266528 n^{5}+178666409398103942369530966223363349938274278621359221212814794998581769269319612700 n^{4}+12568431337902453536280889206007040761321617682972628132954319771719322324547976554788 n^{3}+530457717162162993599334246869861474482952652584525787557385992454493825505029502641193 n^{2}+12437358406930969497887582715779966878943309304959212332008229102792201035534971909146417 n +124970883469980821880209203665810260747381699628484786729916561055973015699246745055288270\right) a \! \left(n +71\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{896 \left(3016390705897524507042275387460532371081345359537034472694203007328311681184 n^{7}+1505658590390757752227258376235208270548176564084689131219085622826900017966912 n^{6}+322084062066460302064050715036362939188805620476182195173263066944105121455074004 n^{5}+38275420442476344972991138586795274112575609301361622701120768494804569127287631820 n^{4}+2728992720864071976532972515561125129229851251887750499438967237665781268840721381611 n^{3}+116739106906694027152202566395175833346633639772415760563107838969092827391730526504238 n^{2}+2774202072324710983746015530236520348200698380557920177355010279860576248091078907967831 n +28252909777755281969211929974216879885175587299093218698329344676385365278164374068421240\right) a \! \left(n +72\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{448 \left(8467426783568838109652398075512880019346562365204439406823621080981268898672 n^{7}+4282992565835763471277529553029535382894722728250350842681306276235165652061008 n^{6}+928425143013435969998539021715482934552367107312727185766194199687888477415998688 n^{5}+111803231238559852556217359323577354326787792058111588236575736527356291102954471060 n^{4}+8077805072024280284530872079326444794933600478397306751522594667813916555678492678183 n^{3}+350157828056031242280920049066302696639532576947780620546070760953607602748909810941307 n^{2}+8432219788761592246229406876115540803465267423781260531207117158104416855664638333412002 n +87020831446498470376200276171043983852016282286660750670492590869633878857771565512959770\right) a \! \left(n +73\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{224 \left(23163511891254949564033287979441877794896872722476739246788818999167256333296 n^{7}+11870584227399936625567021446126309405620873367231803871398785040999334445807104 n^{6}+2607012944705060276241309605874266313452401571923812086842678204530303176312940160 n^{5}+318069382974537266499667497210129083739059688781815898258868660854400823575069120520 n^{4}+23282616519848014492754468027314747776403058903487514461082183842603301436371307321299 n^{3}+1022522426885201810834441454419332053291961479505289049143535048664967654681813910312081 n^{2}+24947163853194414764463860253784128540009654970444799166739775537700244027829931520066890 n +260838932245328083316291043146926607239460473547447948365920455941837013871069557874050490\right) a \! \left(n +74\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{16 \left(432249158966691688557015715146311711986037609533621983536341648552110875004928 n^{7}+224383185412791165387592725128478780397818197382407010898895697352670069509820704 n^{6}+49917102714979180763540569816598135091518228265449729742496344565745959333459987792 n^{5}+6169010505928366375260972817314882674254132306815156935959694432956791140832759904840 n^{4}+457417074675808090456612051980860369029787352857294060574232766070228379488339912960142 n^{3}+20348848754582656873671365880837607992205428712039496679856162606117723507853761346870011 n^{2}+502891222155342843594949176596191761470108444502679188435793533362401042940547397257575283 n +5326115869675657082070218472834314045461350061332079379659204491709946116986344974456394760\right) a \! \left(n +75\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8 \left(1122858567318786963007444945686621850366224116273437494738993076857311431982240 n^{7}+590320586969333906276579018922762056177608768961586755242405808221212225934231936 n^{6}+133000416840015372419541290733675440223759374379404538704504306965847307581774368136 n^{5}+16646557336090384682270663697285582449131348784793852913938259420334452597270431210940 n^{4}+1250045567026377668236787738402314387709379849597328170156735138501029192059832962939340 n^{3}+56319282512439402225488571790722081233657497682488127210274736858171967692111134422225629 n^{2}+1409595005021891061901022140399939781297145033403215875280601419877824842196995298758470449 n +15119350945517750330428517780218720951493023449935726721434429344662778604020320803808794280\right) a \! \left(n +76\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4 \left(2842140603115688444058797590194347824951797125489202109639770341888708597604864 n^{7}+1512985880355716112309075913091168975917925648502977569540248762764908673362479872 n^{6}+345163971671374303878959137826855802141842301371057765449511643605467202569248751608 n^{5}+43744297109766650902776022645571559332313271445202355489485786503804594115659910500540 n^{4}+3326185292153185240233360385604561682890160423917298534977046900995409869727601341045126 n^{3}+151740075951340125401872211290537483490987591790258070557433146405169441307704927540724363 n^{2}+3845555736095881120871488101556432831293198360233156226613517582358235764344389495340763897 n +41765572989897970717194032909074805117721937426020062793957936484338268793446891706994944220\right) a \! \left(n +77\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{67699845898419233783545856 \left(2 n +1\right) \left(2 n +3\right) \left(1758028 n^{5}+19369132 n^{4}+79017937 n^{3}+141286327 n^{2}+93243334 n -171080\right) a \! \left(n +2\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{65536 \left(47526372107542288088789751591062930511975934843847333216896662639960576 n^{7}+19556025284904397948878694475724639247203902812145986443872433112025532320 n^{6}+3448474746583497769687090800781152497112970271023718399543528230432263265200 n^{5}+337814053494915464208636223483182231958449665938979243520470382629388582960680 n^{4}+19854353039814683566306356348769487193701931828574153898362835730737389339697754 n^{3}+700100768279332742638232112256729345831670004350693449121018422733951742463891625 n^{2}+13714116659160863305165472600568873616574148232609156759652209761542575906111330425 n +115125829322951695360282035010684181822383082249190472982632440624077266412526770400\right) a \! \left(n +59\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(111607205546112044583937968983382315609038813768063606100431938230572262131582480 n^{7}+66692617582418287150902196961218840129543849936846039938863950306883680082229964888 n^{6}+17078230203703900700719874941067568975237741814661510588728674887110925464734848584994 n^{5}+2429356170137751259218937773351923115351205258872632483662426043487362746505415967393225 n^{4}+207322225493937788821871649170196839430222855929211567873076525415899435419793619230835795 n^{3}+10614663051692663161051553130774538440029990626151073567891980139405928628468575110510006907 n^{2}+301889359484949855323558539283890627279244345649730526333364512931876106358091906460364962191 n +3679303886771406823208535590252079697267999293774747841177280586839419396609002645494094519240\right) a \! \left(n +87\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(105227936941938188855987665239265020062193128432108544780318442395500782602355868 n^{7}+63563078360959353899391275418374569463948707014674646519821083899405864529162985656 n^{6}+16453433162876808355290560442027051688422135224230976460811617859122324786741151390601 n^{5}+2365862580505021318373244187373749147271573326118404571618544624323356529271505706836060 n^{4}+204092460012224499203156719583414500719628126383347515829612339361136848146472696235798457 n^{3}+10562535393530139871921012812652885942649649570613116866817294336187123533965842782165518404 n^{2}+303660777325492984931440547900387841028570144575855913426524129057175920279467243803485347694 n +3740963872855812146028332696134493462023244944212625197954223366191367350706651670443153744620\right) a \! \left(n +88\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(57867378465552508482085422060972856219907007626672562101755570320515721800196456 n^{7}+33830884045993759060729289777792663966486821470380629568368414638544840620840341576 n^{6}+8475742312015571350973962119242472103062259410837858862896823746482558120503034504304 n^{5}+1179589163040964760983618163500860840797861464970406585979848179899561155731028296867675 n^{4}+98490800833782983333290709849874502852064023091212104929784124445632245103901223747154794 n^{3}+4933690379941379375386548433884668019975237859128079354277473754115908662459893301395519149 n^{2}+137288807750318003812134472963005721210107018407276971397760086210666633933075223154114903356 n +1637120122389197544526430310634232385646359717924521608771317587170716301322813790220229443770\right) a \! \left(n +85\right)}{27313316154 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(115213737376638906704177008087784924130037472978417375411864685693413819545102056 n^{7}+68102427590757825153181152410506529810170701892275865546692408993319568513791271888 n^{6}+17250552170107610092259303139209311898634047211579498631408881800827501105725011160102 n^{5}+2427332090233594649684002848950198920706636690402476792323096467834027783312243803167200 n^{4}+204910564880135379747765712090041179279471133518939282501700130473197425533148453980626289 n^{3}+10377861128318113332889844711520581094855561932797141967603210892700013778776911091886103817 n^{2}+291968051579791764141053914007373263195643497247472463528030547075496465187070322681908591168 n +3519993477877352505054424441349912899229335112122514237776072251756724488310966098304881458340\right) a \! \left(n +86\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(18854312682964670304116400118876871757007344756745688507261811347358330225992864 n^{7}+10900628310374354102722317807306589720333612286104653614611471936480521773454126912 n^{6}+2700722844861819999849486223765376400539390048496310673718490938982354837574578524864 n^{5}+371706369222088917439197303862292959879701292415869803576311286364804760863629835903300 n^{4}+30692678209609284388783417288760546565220390568230181553633186012017229654098263846358061 n^{3}+1520491163189551520864294886243740949393574524452257152132988587255565730681957357852723828 n^{2}+41843028463404989749938691724705252242941500275758641104567677997778935875352028088945797581 n +493455098379281209952789094107804231900073609509528920328969364027020172676413141559469030520\right) a \! \left(n +84\right)}{9104438718 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2 \left(8419255457716590904906074755155569473338429703865138402346582931094597317462592 n^{7}+4592830264210502193217012981062435746940288038848670172593004747853247631957387584 n^{6}+1073706967638277284500346265050502294286817760311315592620800486755071595057955825232 n^{5}+139442094182862688204654740043293945452701473534414486525898904692264760904736676284100 n^{4}+10864964814725349133656633991464075710255837620158746818230200797888777781693200625479068 n^{3}+507912437998010099327891106465239282956220132378957589489827553013261919525084288250742631 n^{2}+13190203691765931875300123050004384147247474882144639990497946506497254367992502564448589603 n +146795178555842666681022922496115768481261147624656422496738428154991068944386481588092511070\right) a \! \left(n +79\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2 \left(9850727246684971831270305196331747758553582038286633946056531565582194902590912 n^{7}+5438366701465657366666672637660321055550370216288241881681311250178253915197912608 n^{6}+1286665516900993880203964854684333813855143192706331017055510494327989105142862678772 n^{5}+169107886512809410814681634153515684566076921664285277616932390760667756065587382272160 n^{4}+13334803009169384279306009217240665322844924265134782448214532977185567395743635159071303 n^{3}+630860949357221565171227447752121735466955381748955773322276358183803690318923376394219217 n^{2}+16579864578546609061846078573794599912179146938839503394902187412287094191297641671447314908 n +186734288188111533950318846877172626320528106673935964884449554668631698053069536542090908160\right) a \! \left(n +80\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8 \left(1752247621946196442217016842262285462544078574092131122537349559868663002318192 n^{7}+944348543713905625820854700683489900691279838343556232409019282178104002638431712 n^{6}+218106818791117336680120328766706988008794910032553711917607294110991080799762193048 n^{5}+27984037645922214106225732419249049681693601819959495772734295006925232137095463865500 n^{4}+2154166648797643421419186559933568907010528281934374094941308133057563164581687852476718 n^{3}+99489175723339031401080804439930242243226899203739828836271608957169324036430159887866298 n^{2}+2552560518717514977531717471500651037544039880614181162272243689032382476898770807959000767 n +28065674293580395267331907082896932443501706106775698329840453917418771846778309587785807590\right) a \! \left(n +78\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{541598767187353870268366848 \left(2 n +3\right) \left(2 n +1\right) \left(2 n -1\right) \left(n +1\right) \left(3950 n^{3}+13779 n^{2}+1972 n -19740\right) a \! \left(n +1\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{17592186044416 \left(13969932749759151455728531996584954795829355683616 n^{7}+2904218387142556171289309910858264237677020266455616 n^{6}+258729774027955764545890957545469516696176246139237112 n^{5}+12804048938384554062346446185630039321391422493143380500 n^{4}+380148354192091280204096518617982419744605419284530098484 n^{3}+6771129901029843781164611320921365195378782150207115632559 n^{2}+66995412243485768039770550764621564146295375447079609158413 n +284052113371261653451835405480480790169808118243663530008080\right) a \! \left(n +30\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{8796093022208 \left(120453712098608335208367035467377193945519108115584 n^{7}+25864449144258282176866982245005633051207146982630144 n^{6}+2380012294955408165483523049971209596700878050749727976 n^{5}+121660566145761359912118531184037998257950757109901058180 n^{4}+3731095497035212947127475011826045038182766905904910150626 n^{3}+68649328555721458765961937600248237566469439092831688283071 n^{2}+701654613274058491583185859623817371950073415689346797193319 n +3073200564986962712433698082858989628781155646814032482994860\right) a \! \left(n +31\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4398046511104 \left(996207285088981351544860627777760154981934814920064 n^{7}+220721012721214124073848762153166048894161778406402304 n^{6}+20957546112909150176319525273077110241074815093183929288 n^{5}+1105456958449607872119051900409647723182857711070860116980 n^{4}+34983983392030902615779349373961542066619638500677908068866 n^{3}+664232777846683329731069752561930156727654223680730567586931 n^{2}+7005979172770050467360449702439632293263211217570202445676017 n +31667095955318344237450191598346265511883074460464319540557920\right) a \! \left(n +32\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2199023255552 \left(7913623386887074100161098234843333967664354304668416 n^{7}+1807486656958555099159967489500045171530808806227209984 n^{6}+176923985079646935371130337656805028340771147460450519048 n^{5}+9620822521065718249790786062911109712731644835062003278380 n^{4}+313886784476026107331779194715000703295947575649066888153234 n^{3}+6144222082972071410008790417513194381342361812685638967420341 n^{2}+66814047872525803097942147623777774438042489777877817187260027 n +311364512571514967794024740814608907054963278212275023004248240\right) a \! \left(n +33\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1099511627776 \left(60464019248891324565740229886218780757590097192448000 n^{7}+14224183737185582468213589019313391966913606060508416640 n^{6}+1434095418570976438791466259528000803902671604446691395528 n^{5}+80325081789164631938075334874807262493694105114209640231340 n^{4}+2699406468634231168504001565946555897922378353732067277347690 n^{3}+54428599424635513940553896776252050710520500613341359661769005 n^{2}+609679836777283317254293323366560742775124454659252743779710997 n +2926751263166999753287069199875164373149059708452052962710264780\right) a \! \left(n +34\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1125899906842624 \left(74725127448538691661259763151349110557679824 n^{7}+12977534908251271877609356998128812263090952752 n^{6}+965667341684847393689392404202376593121180716760 n^{5}+39909219614753726164665365455973426359607921634480 n^{4}+989348750727686045177398911186532225273054663683191 n^{3}+14711350373507103409770696606827556335586102758317368 n^{2}+121494170828099551566543086102503487047285503805369395 n +429883238540622896402827190982817911997010272217538030\right) a \! \left(n +25\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{562949953421312 \left(810409170024890868817713218325358630803934608 n^{7}+146299684089574595636795054684134238502639376768 n^{6}+11316439974628855630635980976220568602131092527512 n^{5}+486188256599548133300247100121301192669631383255100 n^{4}+12529902020004618302073087222445133802684060776285187 n^{3}+193702910269392550130667318754673118719415780670986172 n^{2}+1663193946303516921258793534955944743400695161881063623 n +6118718917332087103451725898273295936239347443181238730\right) a \! \left(n +26\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{3940649673949184 \left(597882312136035613004884331644194441688096688 n^{7}+112027735637911797004437190044335939798836915136 n^{6}+8994533185586944563999500053142185940816576500172 n^{5}+401121513730751673569935319550091927061071694752190 n^{4}+10730948628048541663137116294996228026356151209005057 n^{3}+172211439129379131512351860181625230762107102248990014 n^{2}+1535043883562057614077605896106924858681003787161605323 n +5862829423196437182510552842664732913627077086830422540\right) a \! \left(n +27\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{985162418487296 \left(11780110573057229652802876905363707740355218112 n^{7}+2287897243957382474795016772660648334424586950976 n^{6}+190406232380158117976357967727929281422288127923928 n^{5}+8802064439875316534478049859840773788629971639633300 n^{4}+244099806446577354730082835824851315178221197160521758 n^{3}+4060943036759198307184835927356882777321778638368739639 n^{2}+37526347375084098006227224119140821239734402464198264857 n +148589636618751315844739835123291429366805255475520105480\right) a \! \left(n +28\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{70368744177664 \left(258659574482887917857518757765236380600082918320 n^{7}+52004858919679323255641377173148215705131106831568 n^{6}+4480533334645434852731384320078038617125233007872160 n^{5}+214430894684068075050319540101989039665267356108626300 n^{4}+6156555475563292020759174357379307180496900895194902345 n^{3}+106042084376527563945490494661675404233124593961525675282 n^{2}+1014570532979469457324208323438741609070693746736298688215 n +4159515967969714355458589351715826697649751525585479909660\right) a \! \left(n +29\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4503599627370496 \left(12822033338657755568938460170824911577376 n^{7}+1874115114101638375117786644912563880692192 n^{6}+117341386555823171089033487318581883407933288 n^{5}+4079631008213191893600349585951115347211693780 n^{4}+85059744840736157572696337996355619278806380504 n^{3}+1063545434657602912581597868912831805176715254793 n^{2}+7383945897268819699584293550150839768702048221617 n +21959013873113724924922186990674011143637226056520\right) a \! \left(n +21\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4503599627370496 \left(85979983374143059112738693963390659788624 n^{7}+13159614828393606909769993947906935067092896 n^{6}+862844373688952967451479514732366244555783328 n^{5}+31417006655421224497521076604135402483177207200 n^{4}+686055720863041477589021024785229785441347433971 n^{3}+8984871314716567091199007192005208383278817982084 n^{2}+65342277047208524053230482626794392719784850013737 n +203562742504420894545016028875999628331766188392250\right) a \! \left(n +22\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2251799813685248 \left(1090418634334899040506250937699478571265280 n^{7}+174396493041827775901049109593272656652378048 n^{6}+11949518580312180527789313931788098195802112512 n^{5}+454706531407898256855299948513554831557597979060 n^{4}+10377665320606295169658265773333676612676476691840 n^{3}+142053442931121319622268344909515234757872170216577 n^{2}+1079841073030429289095799385025519184398510985579433 n +3516542365519815902259833900864293997127166977012810\right) a \! \left(n +23\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{15762598695796736 \left(935911879788042790397024882722136033988608 n^{7}+156116747375492984617394730057880381921847360 n^{6}+11157173619881906710509351930122189933285341532 n^{5}+442842527265505402280127251284686404964790171400 n^{4}+10542770341197543787489107108974176424529755595407 n^{3}+150545124894354617892714225506329872907705868430545 n^{2}+1193871993862756715769571422689602486525854725390778 n +4056207287552548443714112355784237452702872049865240\right) a \! \left(n +24\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{252201579132747776 \left(531182370636107760564118240736577664 n^{7}+66624735466998623936651867111652856960 n^{6}+3578771318516457176589429946184799118216 n^{5}+106717629513020418901044512128468496270380 n^{4}+1907915627239651586838939196595221426890466 n^{3}+20450151729487294350276020990886659862844525 n^{2}+121679795028219759141924012917084275187128029 n +310038036690756664557021320364682811549697660\right) a \! \left(n +18\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{18014398509481984 \left(59765700567489846761559038995618537024 n^{7}+7910024823439377382186017478123573767232 n^{6}+448385563875798942428595641087068559543368 n^{5}+14111438831374453023163717549862840479864540 n^{4}+266289845685648447502568532753533412871197526 n^{3}+3012977007075500912228975514338014660110171493 n^{2}+18926300711341289091418240822641676979036975517 n +50916076068223494527266482948349202577366387720\right) a \! \left(n +19\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{9007199254740992 \left(902186263844801238350938264848220702400 n^{7}+125640752122938915273434821007768282643072 n^{6}+7494606303037274777549409645512797595548520 n^{5}+248227387812268841110273724223539338336093020 n^{4}+4930051641691311020464758259218266989052246390 n^{3}+58714984425052880107767475030481895687792161133 n^{2}+388251766354550269821277531379535144834190438755 n +1099603092483474455590924926010617859633138584360\right) a \! \left(n +20\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(101068302238895055423431789789223336604072536723844171112507471125587292970601732 n^{7}+68936964267104650412452952300268664089868546883461471255812461155273856489399637688 n^{6}+20154877418989061981457446621929680464885354879275410609572185800454048799075920663311 n^{5}+3274183093084701790233930876683694768400369412153782414762708327503003993392934895244320 n^{4}+319186095724518163928401088918883235671629917278491781480722194387280238449018984200936533 n^{3}+18672513602725686810892918879954100557260436220214571945589240558077004920575183359635368352 n^{2}+606953252866513491830465009173838323990318372766650945016454258714916213135826215764206996484 n +8456615821756868216561920051514586421374193720234276376041179342241395714483930462734123973240\right) a \! \left(n +98\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(91837719836473913833090425420674991016967960929874891412280319587378054384702244 n^{7}+63481534526531684728683043440252155915215165265489148547430025210124946895937302704 n^{6}+18808241103314551411164717645076949480149074640482108184760255068129471918526453676683 n^{5}+3096184858944977968598936715143952235267796618293210731073534026104216606484438545230895 n^{4}+305848574807489967920044048395549733939655164352850700982380058171020719399738212472406691 n^{3}+18129511220510904121129732215319219519762692188943547254047921470943457910686554592297979841 n^{2}+597091916785787689421633104490473596467922539636710579533538844216052260474037153558517426122 n +8428816876719605644436781412472545037468925426420671353375559956708328421855642769223812692060\right) a \! \left(n +99\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{288230376151711744 \left(596947054150939986988383282674816 n^{7}+62431030730424428856404028361011968 n^{6}+2795134811922905616447773308952919128 n^{5}+69444171684798517619154381578464814780 n^{4}+1033982032621290551598080641973228424494 n^{3}+9226236217158222481283533058681722501577 n^{2}+45681214649389798837235002770020659836417 n +96814278528389219803180473030795383657700\right) a \! \left(n +15\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(28264087385426978677471391108912657444667184445605018564748500553863805097917184 n^{7}+19781896492731605504698844847913430399991039544264242365151964345227824579067680848 n^{6}+5934082697544138687361535067971132952338303302069425922499583167916740874295102035245 n^{5}+988998035581288028072239810913000660716993566464943808802820894679629399468571410393610 n^{4}+98904570291613162165585324102620676891272989312226722899052074159951777519260804831577521 n^{3}+5934929541019978396513919947162435171792102408790587802635688409611329820967706547280517312 n^{2}+197864770872617877317252950933128727628875136243954068199029372171399381440161783385141724360 n +2827287631799054563070105231974652872888516871145934505724036668167001556236445893164625211240\right) a \! \left(n +100\right)}{72835509744 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{144115188075855872 \left(11788523858038241407843997989518464 n^{7}+1314943714205970688408171561656208896 n^{6}+62799769370374601619942958983749227832 n^{5}+1664588829053726899051625052089297627340 n^{4}+26446539092944192536542444254780891884686 n^{3}+251846156498195993265212903882711496836349 n^{2}+1330990139129237859934194922973574317879823 n +3011450812702615378325898113208009562486080\right) a \! \left(n +16\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(78784163001937574673543663602728422682139023389734885033958022086750848660480528 n^{7}+55777666818307975315798303772184575814150087091420374791903742797222948669615365728 n^{6}+16924438761695135726887153409904657047109322411592508469109056229478024499486488202535 n^{5}+2853017410105224608298095423974676659072333248143242867851999527440744309284981821512035 n^{4}+288571851693231377879449779769089553815741495201054706551514016832681467605160860367535707 n^{3}+17513072520575933943770708957098419577534680980182416191567276063943566843335678531086419667 n^{2}+590480080976861527382401717846097848668259388972916447309388628760993299126112176717649692040 n +8532530673472277994328860259176427716210426736050554165630532574391479301759952015816419702400\right) a \! \left(n +101\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{72057594037927936 \left(216660329981387042795377675256617600 n^{7}+25672517985866675835201369947980809088 n^{6}+1302615880188562052031857378873648464312 n^{5}+36687597640920612396237292761350808259540 n^{4}+619431472950459950944104364217321182022710 n^{3}+6269473962232565605882837354992647618180467 n^{2}+35221041762782710599914654843802971636240613 n +84721932780168740823754160218079331552897600\right) a \! \left(n +17\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(53803864833649229478163675099178568113399309443322860185254073771086394740655040 n^{7}+30757439373955904272392377052888089476909887486186425886574671475619782003157030624 n^{6}+7534895205933600033416352849818906622600995167689544709372589252972601377849597770092 n^{5}+1025412227522175757147504592355650011406531262233875819140380287798010417683977051820550 n^{4}+83721570545768678219328561215615564168217297702739594170428527986057219927553259682325750 n^{3}+4101034659142923156353725073823696661221655188074056184683008259138043300386666438355353451 n^{2}+111594436386854214800436105893288464976592462192492723276841589942921434014750672485874112263 n +1301307623541930742446879378310854861596714181248672516340413822576967647900696736984037358010\right) a \! \left(n +83\right)}{27313316154 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{16384 \left(716545876185188469835445803413201335935156872665472814966348029104432448 n^{7}+304629220575320682544394133015656131514754279673871395186642841314181427904 n^{6}+55500735088297141810559229716867777662808388732552197475690734083813291292424 n^{5}+5617323088009793451302603590002058311563228504753621004876213258147707512510420 n^{4}+341104088635647575513602898050183376834025299736133440920964285931634549224760622 n^{3}+12427132110850674279532224521162160454190444783503030320503061039206766871229618221 n^{2}+251511151084490092067589614888000026680299583263528777629927618395122308765230227571 n +2181429944153738387016027457983910846086267470213627320826863757140323274349686519500\right) a \! \left(n +61\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{32768 \left(669029476006122826172645502285522736891649730773643849136294312122130240 n^{7}+288976339515588973462492962554909467082199380237418734375729589437679224256 n^{6}+53490791253717622587904344679708549485556390344799458213680047234155598724248 n^{5}+5500465082893375508396045987770210093622749287659947684278479858485939557139200 n^{4}+339349246076041749938095989094493549088857654095413936472281873435888051630054385 n^{3}+12560910982583350564418783447035929732366363602637236369681682857654380160785635009 n^{2}+258284353691726070358383045268235867331147176829916957646872085758071442807864547157 n +2276004898737283030749038344048517911582778353775157436833126225102242666868527631840\right) a \! \left(n +62\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{8192 \left(4868848174885081835691117355763429272017544109893148421710740450753677248 n^{7}+2136031798400619952261062521302732359309241433321054625947269751390166502976 n^{6}+401595852684460491892213052255744589249070293351544286717780219781428910565376 n^{5}+41944474629713134864164037959227414292121274878103503267363222649102780871066500 n^{4}+2628378009900200978178046096474526960668798514516601765263959530141904204064130152 n^{3}+98816202426651119050672742397172441687458143335845846150513394080285515644317040799 n^{2}+2063819712394461120187472127172876713988182066697287128491114864598673931452720089859 n +18472007235061112107121948109261830745328281063256316961885559560686022090713090594010\right) a \! \left(n +63\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8192 \left(2876752684832857575372638984672091415012130351502456791716659983878340992 n^{7}+1281531897729081838002148229006443315214839808067307066859776467573189956704 n^{6}+244656531173972188392438514764308284470752011326542012009540667934879570082012 n^{5}+25947096428816844365405778934192865228800314703733802342383293284584355517984700 n^{4}+1651006619747437935902495684428024744168267292004167449299492136720568756426032913 n^{3}+63028467514508644024954434733930347685113732477375723848162621763841086072222508866 n^{2}+1336683546617635108252343027976659256032252524120552262290919027526782561356081286023 n +12148422724745675688173076872609648769257282505594423746050439636774385058638876600960\right) a \! \left(n +64\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1073741824 \left(6739264622561242466184061720149308024718248714456917394839072 n^{7}+2056520886546493919264785415466406577245207989299428113835912000 n^{6}+268982553876219229147118421032039987601281706717629494716283089544 n^{5}+19547314848013034008917160112883420623413968168314527841399722365340 n^{4}+852399533675197971838652772690516583609401547282274984995663710103288 n^{3}+22304357829962945353800944055820755931790017873983418975272574349070205 n^{2}+324265118378736862429178357545785622193585483942095349977217637140545881 n +2020541484277329197595928748323133953541774066229973169301691296210622920\right) a \! \left(n +44\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{536870912 \left(37165859074758590290063817720553912410681866958411460870408208 n^{7}+11608615443608133590779133249735565216449799698168193080311504752 n^{6}+1554123980759126738759708587311700947800593753820832386132313790432 n^{5}+115600951376069775604737495256011766600610648723147322475797010737180 n^{4}+5159749919776506960260733686008762818115806235459519444250282055319507 n^{3}+138192549148894231222272487890193305908249554614143039715055946692218978 n^{2}+2056377362265542311013289628888979430493357776538356020728501974715936353 n +13115238026694746354582520734017356078439352148476425965147730829251159200\right) a \! \left(n +45\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{134217728 \left(401393468942098398020308869502988874007462286101295353695252896 n^{7}+128269523292674818674986094346799013264876538978516269100734650688 n^{6}+17568816392887135417310430525353251495702454426803699612392278828744 n^{5}+1336992030068059729515121585308066834678263024915674636405815255569580 n^{4}+61052485558705380761755149345276830231048326928388284111328179179900424 n^{3}+1672874180952176215329865236974433282406881248410171329047215381165330617 n^{2}+25467249615468349188397266713906622137224769801775330769671616730989379991 n +166169986730267867817259499062613827330313453006402094761048171535529377960\right) a \! \left(n +46\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8589934592 \left(103595109578458226931453299017137250088733946441653154048928 n^{7}+30133376651226113578118221237427185010749127594204939593834368 n^{6}+3756854820643269049071608410536137016050439628808014922510839400 n^{5}+260238167972389435085471878557818164511116408171752152270550688140 n^{4}+10817051248952753646067701469818084794137032645806312716981931536412 n^{3}+269796096344623331168408849267499373141437787510517268783696294391887 n^{2}+3738738644789094101911518117714099444671921408390909636259590213065005 n +22206007187515658153428720615019622201030319252413333181595944659724620\right) a \! \left(n +42\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4294967296 \left(597725736960509515324656056884876327478214214397796031455760 n^{7}+178120094438186415179259813972732709831021359890550680598402736 n^{6}+22750654405638735947984852112413673600714407630123095385479537792 n^{5}+1614531986149789668962279172887582997822015025568894331089172655060 n^{4}+68753120530804094673558996026644489853059146222862258072971465270655 n^{3}+1756825469991074392812603055454571537774279693091651627582158013349494 n^{2}+24941865942913090550539159436956339331375727994350357480749878166619363 n +151770204577708862160154441060462602942015212609389700439173712383515920\right) a \! \left(n +43\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{137438953472 \left(231079604086734752522716280871436873360662422262814343488 n^{7}+62338124410960148593971095549741906406541680592622187558304 n^{6}+7207769928469254174473854308505351451339071389025090815548020 n^{5}+463025970141111269531003214956676491217398367083855746964196040 n^{4}+17847963222261616707710065809056078258085921051669421805268972817 n^{3}+412808561399598571464201921706470219867078239881167322235259141211 n^{2}+5304683985333528508780004189825431386060445244690465013452564536215 n +29215589252653110697732874962777001695344501147431026532664519009105\right) a \! \left(n +39\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{34359738368 \left(2885318465003310999094101222441078825416951429755564758784 n^{7}+798550914370150482292642761434247652310816225837869853703424 n^{6}+94726569600981976362474092191355648855467095643057182877541824 n^{5}+6243145672420133452553617097315140072217266882054642154063120260 n^{4}+246898894337637468634167534270017943380420528676002109816059282056 n^{3}+5858907142528620879519957868539676097143157811716972830589281272301 n^{2}+77244910545566634091856237805119527759063047470873042766397228255581 n +436488069185277339058974748420505214381269985067394589839215404306720\right) a \! \left(n +40\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{17179869184 \left(17517298011857070248143093473135755891436760451979985408032 n^{7}+4971385969172112437722083182339313760130256561807344595925600 n^{6}+604717590500403347552260815343051308065134301531498484787314840 n^{5}+40869045835450174738911436293847162865083927547034181683446620540 n^{4}+1657389698696613230499086401467542150702455773922699082016722018088 n^{3}+40331158075266412280215211220385413549156869299260972548656533201565 n^{2}+545276238714406313555492751068819679099550255973693059027566103816785 n +3159698449763633654397731941239390731401379468442157526910188456770980\right) a \! \left(n +41\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{549755813888 \left(444967833551602449630189038609227959849803139144721216 n^{7}+107731514356096082696319967975561778543351263432877018944 n^{6}+11178542287943095294530111922890267698955096826339341002680 n^{5}+644403657274119711473936655659367959724031895569793550986500 n^{4}+22288602777293428844182568776107625505295385624422458476708594 n^{3}+462548805915491576053002047072784118234647164002994106157083691 n^{2}+5332811597428026040891841860797921098841938451073266124785860475 n +26349503245848813670444002889985090554980653906739535640595225720\right) a \! \left(n +35\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{274877906944 \left(3158671216434912003731871457801634084544337999191080896 n^{7}+786470303377912936174707547198838451468207049862675603584 n^{6}+83925881906161552665496330169703285163033697589067652827768 n^{5}+4975621981971678616845587289688289732901136984429198878485620 n^{4}+176993931744822715641387725504481171849317614328612730205383994 n^{3}+3777694159715319639950201801686777732961796649399986023065378831 n^{2}+44794712026419456268198884234362113361683984102563841506583397097 n +227641702221823685765125445169431670362672321076773859325079971800\right) a \! \left(n +36\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{137438953472 \left(21661249217322499132240974743826702788911620774043557792 n^{7}+5542814253926113947688134719388789386085173697684598934368 n^{6}+607882706374999569252911792510163522962255437551792649660440 n^{5}+37038561551133003952766942890594169014389085917511613354689660 n^{4}+1354113192972497872731303428067397507221219163677722209693083948 n^{3}+29704364047613613708248080746949825929053267565852468534750435727 n^{2}+362012949974641655616622629650220909617266382397990679175608178475 n +1890863166000472083218887122455086178079899032420475345180410890840\right) a \! \left(n +37\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{962072674304 \left(10266535749688633594603171333599741401575147701253509360 n^{7}+2698163941017299155906226823649621728658872324693455650016 n^{6}+303921809723681910305864343639805630319896460366170784676072 n^{5}+19019834774678275274321783087594341981139919989719092575623340 n^{4}+714207848873807310619448739314013154348229648793703963341028395 n^{3}+16092124642095308212741524533250824813582236244880237678219054629 n^{2}+201440669948734587269594921141326721934524282479444565480202942048 n +1080735696875377237729352045010475049274834460747037742916288938930\right) a \! \left(n +38\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(77251350193228776716927560462204313978726442060330423734371968189244505471797058 n^{7}+50556671516641001812598574860946709313121511332801593014217390029812361858549650816 n^{6}+14181137982855254137491875509928060060372949396843160530096890701915261934061085209893 n^{5}+2210088234415851627614259689089839858802296381314134499014773663661767361004474402741805 n^{4}+206680381481611102167782996928746483178795989760812482587611827432739977783513483745598332 n^{3}+11597955880062495364039810430032442381218492006655559182691338991738187476361094117552561229 n^{2}+361604562455462135091167513032831876382266504702815167341423446904802893573085565479650378527 n +4832298774568624770108332705395116963417157880393991272155224876069469554975459848473180653000\right) a \! \left(n +95\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4194304 \left(1359525448125484464678063715340224719674035148249990575541604919104 n^{7}+483417795227784172123890129425576526339536720189476864806986414358848 n^{6}+73670070736275053208517731197397392740891878576253135159399992398369160 n^{5}+6237271920773317939429794102796032539553309262405004823893195652088124540 n^{4}+316850870471954690204051065378024129498563240823171770841564857975527861046 n^{3}+9657607632553301156933963973652748791325154638175355901824889919620703675677 n^{2}+163535754774254136572995541516021794850648433093973724769227439107558739722085 n +1186801272487912038610728634760230468866099303719369175502631465888991556819080\right) a \! \left(n +51\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2097152 \left(6489630317901672723044349564127759866949555056128478440710228437440 n^{7}+2353798096951487127789443949485490682812528972899117450105423215975552 n^{6}+365884999428298825081073558551407071654713196794190036767867945606735592 n^{5}+31597183436190721668850543224261559709499605952041013986207861502907592860 n^{4}+1637201943766774264791536367921596556974182859771996247978974310538839828710 n^{3}+50898417627396550013112089881539405249362266256094641204267962317065355234973 n^{2}+879080786407942480244679046091550009217472800693905661537010177066554553147523 n +6506832488908726067157389201775340619122417338374790283243512426423738602400360\right) a \! \left(n +52\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1048576 \left(30298428041822560502533225030458493155149564729727346330677960966560 n^{7}+11203880205546825571491838510455907972633290697827958508203055066195296 n^{6}+1775565274958939926029359938899029059906246640289205877130283282438374440 n^{5}+156324530844134376255876645183267600905967968152864380416507863788135734740 n^{4}+8257753750245963228011972156427745800961883959353705974751755898284737928480 n^{3}+261721446559780672406305177718636812917893871181299462154259356531229908652689 n^{2}+4608226994597128163826006507129191797821500037610936230387331508860659703202625 n +34772801476829809806932779283038042334049200811023464506712625276808277869249480\right) a \! \left(n +53\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1048576 \left(69127963149725767948329327616265782616545063740919492498832704427152 n^{7}+26049193596111845752678678832040843115916244121448659652894298145430048 n^{6}+4206774017061924474816993124581960743633631633974431786750892136289716880 n^{5}+377416766663709460609215413942664511364260131688060319411060200228328971400 n^{4}+20315735522822143538827716556596485718637540289203339603453437029202264229723 n^{3}+656117764683427906100721177402944092979945262798921528764345682565341337242722 n^{2}+11771823597801478520802132769775945823295504233036938762322070214525920649624355 n +90513369084899948285274265181486807743492539253169715803003083575740919691756890\right) a \! \left(n +54\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{67108864 \left(2123766514929156247041669152365569258194961407194045387702218880 n^{7}+694019080659748198889846708639237802225858843122959108899357438208 n^{6}+97206909474597664264799698990103196666956077582876282100536529264536 n^{5}+7564589597140743908226577309030558955069204347561028187187372991860540 n^{4}+353229556540392751317730404356904532600161886720445369876879288319900670 n^{3}+9897130932656154175308789064384309414028213085173825487254899852454665177 n^{2}+154069142694521410880812550459879273770818570258666530331854979037954982769 n +1027943035107430751823713699133253402907427134563615209323056004986225875060\right) a \! \left(n +47\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{33554432 \left(11013266143830159105153061409921589200105993285481596744530580608 n^{7}+3678574434062934879811159934487449520215480210677824697232108398080 n^{6}+526620745195635762692929176112887648389576342073466610634319755659320 n^{5}+41886382358917102584302332649171342211629301418269962454336698832323820 n^{4}+1999057073128436992048023417609611829273434087774941160427627880037455822 n^{3}+57246934816841636072757524967411407471544397961289284831669819377832024805 n^{2}+910809434501783246448232677501249284921731348734220739591980410745527675735 n +6210750584035007210509200559333434095700304576961419210899558161255619198720\right) a \! \left(n +48\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{16777216 \left(55975097444365063596613980233419854602104547763600362874181255552 n^{7}+19100215178432054785436229715026303465180384602479798184197400056960 n^{6}+2793377767231411221092738136889331019487613513049131920714404695329912 n^{5}+226971162109442816108938429167110489471095682087450625429839957109535540 n^{4}+11065789018427962997472633170871984865469191610915103323871736023123892438 n^{3}+323714511810205368334826728695554271145214639523864767536612968716789352475 n^{2}+5261186562561727678207163874464548794236225403118247147529031241382199380333 n +36647147694838374159185074863439820493074116372128210874106277806743209171360\right) a \! \left(n +49\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8388608 \left(278754706156220384691032993260397076925893750298229232897227234944 n^{7}+97123226907794924542091694325831297737853475500402635985068133191552 n^{6}+14503224758170780942396105899985018044849949887649402593736290680688376 n^{5}+1203229271191050230311870666285828762735371446646590901752232611186680980 n^{4}+59895723331672021663259208832143653786915754014293419940248841777556618926 n^{3}+1788975616520871109857765347558191209278437970048564935035150636071942779443 n^{2}+29685753025237591218167122126786253625151100659704385069961069528229606572019 n +211115512154986577752123357575154298086233582822118655592468334864046704509540\right) a \! \left(n +50\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3206630771 n +641991095449\right) a \! \left(n +205\right)}{12488942 n +2585210994}+\frac{\left(1428639636162189781165667503460850539444275094853086121312873478722258949093148 n^{7}+1163169171734057829980567908560395637639996740334766120266864851587091578371519936 n^{6}+405863516755304534185866527381610576342615493475850260385627690429179406499524619994 n^{5}+78675293817760487694167256917951810631557922829705975618049148803148875561287709713605 n^{4}+9150434612873394128290626257423231634929028321766158013875019796479675316889445182654782 n^{3}+638542876784057779127683840268701722645975056028053655562191097750696701665435976831939459 n^{2}+24754813005223532468016434914953236840811589074955861730155753059223909707849497970952986096 n +411288155397597613558918413693866765628215016186227296368385566880334707304334798828444418440\right) a \! \left(n +117\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1778907866868173329560143794733935128191671612533496821008407516212583056832760 n^{7}+1460051776586864665419013728517413405517344051224312636913037808553872247118993408 n^{6}+513571151110919690315687414235110489393096510310950395994122764401699540142867364871 n^{5}+100358654315470291706830920138773122222917683050783029925645511064989326763717244521920 n^{4}+11766699010382232093647548297747062123731341620811934010144885668027042650795010913582605 n^{3}+827751676657545414832597701428257387835087193379439697350817972838250744586090998144737432 n^{2}+32349483516817487904087718067745389504323636002754512282309647277005619848120883347455146924 n +541816483849355180387407876380876385808031340563581632435707557177606654789695272532419797880\right) a \! \left(n +118\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(6819245078395551549924103134607216999858952088180439788785108967951809045837860 n^{7}+5462765521662696786549699296905840074509426248432431530297434996712735631382991600 n^{6}+1875444464133817909869822005937727441527364780392749242296749822059029678859537590952 n^{5}+357697200175313509499194334311931826640945359062397544466445663257723515435161440920595 n^{4}+40932693922849508596738967838521608636299523561365195834351604075731938149007991917481790 n^{3}+2810402900211759658278832338771669501080059373430119477525166999343312368447877918647147965 n^{2}+107197972320572079680253868642586292757432901190422650557082509774307471918221751025249980998 n +1752346634858090444799510888460772880026868063287068744813340246768321929332626084048075217480\right) a \! 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\left(n +129\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(917382782794921403597797959641763508763851967058226079018125694557880566008 n^{7}+827709467603056955302478384419600358822954353474637350381795937453244567559784 n^{6}+320062787281448691957954715909430069493106681796645325954514122424241400869733324 n^{5}+68758567160719063399173908663134609862983827511353676224931766006547668425881062045 n^{4}+8862918509199769917792787445599922689912796062788165867724558141819767709872148404762 n^{3}+685464821180281177388569924256843266236283024791527105541514868350793950927067913032951 n^{2}+29452928427297682199152806697582022076818761655455017676958382923748433169591823626374926 n +542378647155462339524811135686492060111794909005315366630896055825888857019100516111386360\right) a \! \left(n +130\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(425989646330806182502269371264892293931039493393276662980182964118160413620 n^{7}+387400661836764519228689206741778384336528592311280894178567322423962720937704 n^{6}+150991888154316164651471134791306720428834653246589278037698009655094718512893018 n^{5}+32695146196843498543566027656096124143083770567778210622656201292279825096685515935 n^{4}+4247890410502534838133881719330601191016227436899546034921701551445763218600238591180 n^{3}+331149317971594784871616499281165041232753789335990602511211334358741834994403119282561 n^{2}+14342055508732753234200250026968774237050124313996714390841950623098833409093236730695822 n +266214566343425195425824065633434054736908760535398298418404373455950138662168079731501920\right) a \! \left(n +131\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{5 \left(38941732538129284059835451927350077014642453332898989705475932810736241988 n^{7}+35695943638135462598374794705767736468247448524548092247414049480914692619016 n^{6}+14023498898947184117262775426960873470975319741486173644167413204738675615599191 n^{5}+3060781279724153498789441649298486315127370788002831140434752822445568070448808949 n^{4}+400839537296392235848462188827496345899479427110417454996528188360276348621198014175 n^{3}+31497156337122258296029064123036204669282045313387864681654924128739112239150409311199 n^{2}+1375026655416372197691846580956043748462304279898679909163048313825198982916558559420362 n +25726800559341154551623206604615423296046955359344351720714242293893739092125320276683776\right) a \! \left(n +132\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(672569331906089000984441261887367919609838012888600126740100813825227610702 n^{7}+597344674221811997152972200663016090652191231989381398343510665520137758650480 n^{6}+227373121455201306911970292603949843445379384734645866361853321895851487759595912 n^{5}+48082147325020493026658209219257702403916799313733285483323395978606447171575303055 n^{4}+6100747844692991519938296084716720583307289704593089840025661131069139841023143631348 n^{3}+464447807456007900537008627305354120883957835009921208543178087306356407994145247913455 n^{2}+19643630559378902694451312654996235259874135649975158092323859668286174632030680218262708 n +356068414381350235542115932659291041803571930561338429969573187940910171073732540271672040\right) a \! \left(n +128\right)}{72835509744 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(32022748500908808466054820693159596936893805870622343673040843815806897471804 n^{7}+27779888064878145522668820303127386380624301146618987888208853008523649132488472 n^{6}+10328196879631054683134210555048128246920740589619903184232697912458772259561017551 n^{5}+2133265946381681011639000167604639924847344658794147183300914608566196743014027145775 n^{4}+264372204089748176790911723408315932495847250710830500936647602762175212044245200842951 n^{3}+19657892160127395466790530111882621384902837326030491693407155446902991620031567953594893 n^{2}+812053760782702558299725840197895738680738889846857987977572197914539681694490925619442434 n +14376563284885999355803196971383396099076957948813953407779254790310387954205747706117592160\right) a \! \left(n +125\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(5467957069648141719279863076610301602778049401744923285389485618190849078340 n^{7}+4780800412234082702196855787619088307176279079429120878174143346064274361685232 n^{6}+1791428149243369701795515040586672668116212432326622621683658845011178467517510263 n^{5}+372928698051111695129795913624423503422814782785802408882188765349162117825833349020 n^{4}+46580450858524751011578637791055197252674738413159430775930548940878882235808204986225 n^{3}+3490865608138837502388597413271119157576666357495856497929157294435742497397825981982248 n^{2}+145341775878686708205207723724365597877964631012263063544716491893043124341239505003408752 n +2593411868166116131355504396409140573644092658878255218911194159143832067150279820607103800\right) a \! \left(n +126\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(8221490483642587745980524877766174609699656596877717792271695286083953785992 n^{7}+7244865032356329071359914913099799137593453944533156958593971119013003797419400 n^{6}+2736116943954449622667422765778436423500911735901979705826607890684699476069326633 n^{5}+574074181496835470940943634213013286601099011778547201988141756328336609957844348335 n^{4}+72269365571994497206036304900715852041769633625772362418122982134449212759543937432553 n^{3}+5458753022306117333588875261640335765208602168483263450813254705965818055057103919549125 n^{2}+229066710392526337760734721489728969985789186506474759327800685095482822706237797347703442 n +4119605917262367212852490807108412028304857960204043564187780680069452809046327647831454040\right) a \! \left(n +127\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(61113059588362669961645731142822136327391980877832691947786387529246660544000 n^{7}+52601662928092803133955707875693772700265927059487870773998452101906371436255784 n^{6}+19403769641821994457535855453311684964387327611078053305363517217819334557869328814 n^{5}+3976475078598133727133401388204971825416421350278024917539366639629905757630558353895 n^{4}+488944700850256991591417048757179941801955210622962110268653641122700570286619105787520 n^{3}+36072031019562857097588347753473550232055458240304954877553853114206605945308009816260501 n^{2}+1478451613878690302302436515182762703959146845230006117938936873088156463499409355651845606 n +25969588804347727985745008508209271372776601420094004252367103817825005864066868648675493720\right) a \! \left(n +124\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(638666874262549284254233162653316735845207133623577252751724541026802238246884 n^{7}+532632288761485382375080068297889279177920869072117560360004130393066715655135184 n^{6}+190370316801304664041490943707719956510238762612649212516804849154375584833587082904 n^{5}+37800183459428972137880582697642298781049839302898589106632823021887110783165028888765 n^{4}+4503345626999580908678637744983406094895253262825224780350713689701758179253744406085526 n^{3}+321901765075892660372557947108598885434107411243630958338343323497853658582141403800743811 n^{2}+12783047274924402544634471984981536848023554591504181881997660025459068151019519357394466846 n +217552520256564990118850314346999616126432798217318124210284092240787996581300937678424855640\right) a \! \left(n +120\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(17547469874166595884323314353249401676606327581115059846262638275745991367000 n^{7}+14750732364996251168229883194610718125976907520854156746996821691342852389639792 n^{6}+5314125863873739304951118123858004720341537087324309587996531827692187364121849500 n^{5}+1063588322007419217192851272559748645509285522004612923114663370530482350247789057505 n^{4}+127721063311155605091052294164716564514981440175038361015210076211781171915438190168710 n^{3}+9202349999928452965364555675472292100252328213534634981694228831954561854614987714181383 n^{2}+368348142506707488870104677954334112111233469840627982940518595354226279338843157542462110 n +6318841632004896931700940054123669371452716573336171049352434344175433573939168727772843560\right) a \! \left(n +121\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(207417367871825173424590976853571341630091563977705713452334653082597683982424 n^{7}+175742506431974310512195223983385774312203129485005140361955973860945105657499616 n^{6}+63815806769972604409573106032370474752210958340432604865624236461358684120994657186 n^{5}+12873711342401950247416123569567662820944144294627918440459964348993392265997656233125 n^{4}+1558214008415593410633793376915840032259312654487356814146944683224688287990129974897796 n^{3}+113161396840241712609023744871989980398324500701787817634371740575792354997334542406709959 n^{2}+4565555441454900586587124548590898583936200014953376688862899338687362106527364977811790414 n +78942124764079346292759035037142071004376944052193053229938697470486814369907463878979961720\right) a \! \left(n +122\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(113940381832936816373952659547112813898626865957099945772525362107231975568168 n^{7}+97303995249247655418061051732972121373554917263649117252266449163352155485426944 n^{6}+35612632939718580298110241885181066857457712464400052291878145549515771959965105322 n^{5}+7241061211499204377051521753248545510769095071089685245798962215304528063829947024975 n^{4}+883382658015592742891469112529832385855968975628150310516732269990196159190811908736172 n^{3}+64661246152785661773065210652412796887846135221313348497802329347321131191119640353207941 n^{2}+2629445060194769499401551507798384001658913376581836940156857933048703994167750263722599638 n +45825236725864214323372399641831462275493624857427952821754650633773656339279240891781982960\right) a \! \left(n +123\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(1079500538291487366774642926183490932304637548134485437840005532350053891682640 n^{7}+893130602294857520032439768170063699185039645006284234856558653342269089636398248 n^{6}+316683323880833545225592198861783726566252578435154136956250074700655104932247251398 n^{5}+62381788509789780607238386471050896498214648006000578482295208637167644891251118787055 n^{4}+7372870626639787189426070884086481304024588769638581815832320300271577941333773672030480 n^{3}+522831293114499805695786406150763489309441841393215928002863627520300583327277581338909737 n^{2}+20597236327544734649401813050125611587423619334326360728148191446201759815344232327633585722 n +347755872568436699328582124841212786589528735657872047526720765923716767584209383563641965080\right) a \! \left(n +119\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1927069094386999028040 n^{6}+2285886061926617871176024 n^{5}+1129786047206879473059835323 n^{4}+297805111030086307292634908402 n^{3}+44155642397567157201079599954993 n^{2}+3491681311666713881641278280304738 n +115044896916089570711266198534656720\right) a \! \left(n +200\right)}{5395222944 \left(n +202\right) \left(n +203\right) \left(n +204\right) \left(n +205\right) \left(n +206\right) \left(n +207\right)}-\frac{\left(312628341439839024 n^{4}+248477594016252266744 n^{3}+74058490725175604210325 n^{2}+9810190514110523114204947 n +487313879641418977211763000\right) a \! \left(n +202\right)}{1798407648 \left(n +204\right) \left(n +205\right) \left(n +206\right) \left(n +207\right)}-\frac{\left(17525921273035561582343149098 n^{7}+23836039988498768599202241891332 n^{6}+13893316117257728805968713375103379 n^{5}+4498840387259573149096679764091959205 n^{4}+874061269849858546380243070097097328647 n^{3}+101889587643786421292717332469489568931763 n^{2}+6598430180774569794112296603850713577536216 n +183134460137908390173801413220547708574905800\right) a \! \left(n +196\right)}{72835509744 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(210564873451668607102729468 n^{7}+287805171730477004415770193672 n^{6}+168589133267877024654824150349055 n^{5}+54863456758514014436235777522668790 n^{4}+10712309932559934823625053034849690197 n^{3}+1254958818549481945291526227742326723818 n^{2}+81676752069897909341151560214241605135840 n +2278168354002148757651381304798518459016240\right) a \! \left(n +197\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{5 \left(409023831911623025164348 n^{7}+561839235479139834685710416 n^{6}+330745229622228786093460165357 n^{5}+108167670538935784481854177729169 n^{4}+21224989980598249877717657271448981 n^{3}+2498869923374303011659558183446341703 n^{2}+163441447373847539052640040163305775474 n +4581406979201547242212085205504285068136\right) a \! \left(n +198\right)}{5395222944 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(67433342051029302255896 n^{7}+93085097057813891221138416 n^{6}+55068527909652838811020049189 n^{5}+18098763568547033681870293257000 n^{4}+3568948154829500395939252550944079 n^{3}+422257598319245727726809195507128584 n^{2}+27754720776620187360074105290125354756 n +781833249156952089713030110062538056480\right) a \! \left(n +199\right)}{5395222944 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(63051154156626909290045723976559744 n^{7}+83621868687751581426155310758733118288 n^{6}+47529873742819194908320382237957842061371 n^{5}+15008514732584242299951598074966592552288710 n^{4}+2843523409597939066806056269786503039610466361 n^{3}+323239149511331579433574457411673628779692378582 n^{2}+20413403550101216793383472596498641800950352415504 n +552493208251226074520642709433989522888093645575040\right) a \! \left(n +191\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(1798592629998580042946304299213792 n^{7}+2397520963579099007313681816649901912 n^{6}+1369656547294129792487624267978382278438 n^{5}+434695256029704094939820012154985688471135 n^{4}+82776270286294118995264716611389270734463628 n^{3}+9457460928233162116596688401040878259326092153 n^{2}+600298512527592492760651100642656772140751672862 n +16329757135837376402745501056926980133942188595920\right) a \! \left(n +192\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(773575478331159858079970853252964 n^{7}+1036397113570459457113564945466112632 n^{6}+595071381824068245857367734402483460490 n^{5}+189817216400846434581025951967880997987415 n^{4}+36328676249341946736051735742833625000287676 n^{3}+4171680116913246332520127743124798431958104773 n^{2}+266131412884476270174315109175748325965135903210 n +7276134689147984528685464501459003134791090624000\right) a \! \left(n +193\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(43656280231494935878484382770748 n^{7}+58783495936762184547813864857434336 n^{6}+33922135364435951329827303261386250351 n^{5}+10875127071158950293113091815985526672225 n^{4}+2091860180227112533088670405867249911006127 n^{3}+241422718541625589301482120474619733064949599 n^{2}+15479147860735835996039975285735390632005996174 n +425338922017375603972515378438619283434653209640\right) a \! \left(n +194\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(1124892890812304003081986379636 n^{7}+1522286591757704976507207106685244 n^{6}+882877591060587414104348297141799671 n^{5}+284464241231798495296181986820374967865 n^{4}+54992283339463684630794232854115506708269 n^{3}+6378561132299137526927354201009050253517621 n^{2}+411023684808696350483087521720139193839401134 n +11350888683361597510943005645747477331486599440\right) a \! \left(n +195\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(4697214630827629055086261752087046727048 n^{7}+6103245000754395457557333134839514529667712 n^{6}+3398619379672115572656967523628429658932946163 n^{5}+1051404629100246964592647630493673344820372239450 n^{4}+195158130265895466647164411988030159342371626201497 n^{3}+21734659683221488618505808164588293178586007799503898 n^{2}+1344759869098689872049776550244547815805811032659304352 n +35658090192873947447071195022399435880125937658108117920\right) a \! \left(n +187\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(413825295392979233785578507079077246744 n^{7}+540479593728695122001205251766882443094320 n^{6}+302525878029538564759851377394988921087425186 n^{5}+94074305712368742254218846143540641954175352595 n^{4}+17552078565282269213849488417023289260686502708876 n^{3}+1964876005864101154937813340506660015775277333593425 n^{2}+122198837319723076711447289689148028825581279827096734 n +3257017332076054839765307492535628180307502112973609320\right) a \! \left(n +188\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(34165812256583797249730955229027801816 n^{7}+44852361683705725522893321690278897533264 n^{6}+25234778347577789884728718705533813761949583 n^{5}+7887485747191604018840525730240107197772672875 n^{4}+1479198204733589574386958343786725160594264012519 n^{3}+166441977119522251491503248227450295221718311095341 n^{2}+10404574824753767195045841942599890579306444055169042 n +278744641345306429621141973403713268818583392822154720\right) a \! \left(n +189\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(94104340953222686109596111225749012 n^{7}+124172260238250394249170131256097944212 n^{6}+70219833756505725348125797162951026652216 n^{5}+22060715243054293244610571012752972885327695 n^{4}+4158414123176540505006381375637055767920959938 n^{3}+470310052467806547455746425179311859394654036833 n^{2}+29550540316822159111469724756567192459264762098244 n +795732269823807800095283509956465295523734893691590\right) a \! \left(n +190\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(4789678103901355255515671058807126134059468 n^{7}+6126715613532484312890472023041227074457138240 n^{6}+3358703557192646289320691767668084396020819042979 n^{5}+1022921935369382253190126048879391316582262772796160 n^{4}+186923522806775591309646505018402362897151350578757397 n^{3}+20494442014124798595598614651241183528534756938208557280 n^{2}+1248346614742699457868448844105299897620054266283857291316 n +32587944836180155853688077293653952422248865002063528421480\right) a \! \left(n +184\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(503949651405709282868162737546701941069712 n^{7}+648020005297773634404136908785219165843002360 n^{6}+357118047616680558318930892343295867200521324203 n^{5}+109335604661131354036549067741063779334372550287665 n^{4}+20084528106803655384035597194830390341257929817470243 n^{3}+2213664947851814577881580837443305431034844759889472975 n^{2}+135546606683280892588245367744205068910257651933370208642 n +3557031102733258658753418619802122995320176665706408468080\right) a \! \left(n +185\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(25056861826114449690190981573362631392690 n^{7}+32388720038498049352648708051759887290380216 n^{6}+17942485545337733301464322760742886015306083067 n^{5}+5522013210258337329772918402861828566792419244535 n^{4}+1019675711011352564868835529676936214402972088382705 n^{3}+112973485798545240483250919587956513331735573934383429 n^{2}+6953718004744144737807168181050578576824943764926683178 n +183433839160329364163851508203409100796390032513957550860\right) a \! \left(n +186\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(369170188517581816471395292526827447611131564 n^{7}+467237976819780361308972696549995494075210361680 n^{6}+253438843732683934546696050385150396041367394522684 n^{5}+76372334503594445387936187685377839855862655020792925 n^{4}+13808629715170705586918774935165738457343172733134800326 n^{3}+1498017074039517520642263534984536013663345535454000189695 n^{2}+90284018263544671929171972118963613421607367637781895206446 n +2332000743743559846139721888801021632604288662491827863407600\right) a \! \left(n +182\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(43138734202252813245124182155746024779783992 n^{7}+54889971114885382360855342329702633223533738680 n^{6}+29932406382935408801593668005128627484196091520723 n^{5}+9068127107481695423644634754880375255237206272089085 n^{4}+1648331982447554018526650638300864709283161599302857183 n^{3}+179772360531940225019245413976894539689388602187079441115 n^{2}+10892525366621458467913407763022348381734874805531271416582 n +282850799884622105958118251328131582813490251062577239032680\right) a \! \left(n +183\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(23448279135911596513401706105346665328488506708 n^{7}+29358052912999305156605993849661886852983619829848 n^{6}+15753178722095586777417668124520681619617285743953391 n^{5}+4696108752061960794572597757351097831307323028387891785 n^{4}+839964394795830937631493432968566884951972182444288592627 n^{3}+90143918085176658282861190743520006326700335161600842706707 n^{2}+5374537367404125536021815121433713748228978411340145684055534 n +137331638361554722914383426038594664371394308273966337820297480\right) a \! \left(n +180\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3009995243945459768984418236523910252224626748 n^{7}+3789151900797105621840602400789777229903535669144 n^{6}+2044289057032683733671532923968708778448182031813911 n^{5}+612732600130805312633716113555560054093755782413868860 n^{4}+110192454033853339677183452940516509171311529135795790597 n^{3}+11890084483793181298771886870792230344376792499261047290596 n^{2}+712765255372493953250133220532491787237376828972847751142384 n +18311855421926180396129006177025622234942699176599614933873440\right) a \! \left(n +181\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(125925390630917746057824185088059817420034841824712 n^{7}+153262070784974757237617966418640471272345797681714488 n^{6}+79943670413753554406663819195559277121741659874847109465 n^{5}+23166788681199725293078826161593964937458665727933146985505 n^{4}+4028132710731112493753886082250658464084604364879882216800633 n^{3}+420240543058761316914838291886645517607177039742342821265699607 n^{2}+24357049742594654364713042870654020868019409570374641555705995350 n +605033967739022684348589417885346496449527232911914585825044530120\right) a \! \left(n +175\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(4155028699126928736997880076425991954831648877518 n^{7}+5086624290608156912895313247713838246428980315264416 n^{6}+2668779441159329390958957278691428497598920562874050769 n^{5}+777906558185622653782843390970835104701746982153004281040 n^{4}+136049741736474141424045874637805793775929333178139658591997 n^{3}+14276561047175584065643471301951861101179974675693397249389804 n^{2}+832302863992007921262481224047095042497308111663996599141928736 n +20795379238505981687788296256549654840599155076275354384714984460\right) a \! \left(n +176\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(8690865607810357659617970733818698182972767969352 n^{7}+10700736612331116521740049751862498474794820132182496 n^{6}+5646651928521175062379476881297141938282816615035199963 n^{5}+1655386442901870836817273668819379345171509971153657579390 n^{4}+291180715560201075804267807987911137014631080048215615574013 n^{3}+30731284401040431148979557729563385127210118763163733393147034 n^{2}+1801897142623630343890700402580892675184479469846197420198868712 n +45279980633596281626002102963629999221131402606068498106684696200\right) a \! \left(n +177\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1256037242690621102803944692650538234330884557328 n^{7}+1555284109842405827420992365359982203902632895160136 n^{6}+825359120776849790455899820583578094787500106747628924 n^{5}+243336076484907637572942414548425082314062000958111018095 n^{4}+43045144849439763567512736903365930388980375721280853895322 n^{3}+4568735498020602645887465696196136007370664917447156007477689 n^{2}+269400449600455890884141574402998596081356330855903916956807786 n +6808114297686843611308522610176700744969547351664760728578090120\right) a \! \left(n +178\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(25006098825369503978104746415460763382429065420 n^{7}+31136791325680049860772803432397894574846282656248 n^{6}+16616023184072138841429782119445831423720154475869420 n^{5}+4926176445274225045552537989872956936670875176807304075 n^{4}+876286805900384444065218195772068543461786221267368175170 n^{3}+93526796076835752172078094306958076824511610549631416466457 n^{2}+5545690145656925310251790398772128438930138577678060254490090 n +140929094757164097515365190275403606772193331041484355084106200\right) a \! \left(n +179\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(14704482250948365979707677468321594189355979068810916 n^{7}+17684537191542348035840146206118144779602306394115257672 n^{6}+9115206048242492728984846822661890640412279425350322805613 n^{5}+2610192153056572931771992456277414129777895344885531285961315 n^{4}+448472182117650738300647705964991628847257465826315791903793049 n^{3}+46233382413784890316282800878694936761705083854099662199332863053 n^{2}+2647946974526179455211270881779489293114265403485350112919011099862 n +64996828550800626443880732085654106004103300443449288583290178242400\right) a \! \left(n +173\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(2386900773259723948548091445571592292820388126098740 n^{7}+2887910957075774428728889382796617840803489672451444656 n^{6}+1497482458830073455053880967160092353498569589160658133887 n^{5}+431392467567262720895613928787759012875045130922789909148990 n^{4}+74565866965091557085596204823564327426536440354291908417953865 n^{3}+7733291158186931224868231726899548955051811657035049181436248094 n^{2}+445575956259738399214175103917727578931197075620209515419436301768 n +11002921776463633393943485567753731139677990573169389856890897018360\right) a \! \left(n +174\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(16758051022517045356830067748518583896750684825960705600 n^{7}+19667804263238494131377820206361242548193201367826853264256 n^{6}+9892729727464847513733918566118886312212207891964231766239552 n^{5}+2764449797010913849031069045761971077350225920521901313701797655 n^{4}+463508221709018680567933609596525993333786598830518816876888995210 n^{3}+46629683488462079195176769523848458538338526929392195544029564034509 n^{2}+2606154441033861159163107457548290777490197630254692169021363398520578 n +62426117423077391586465645140114567898374273890277055987776699999318520\right) a \! \left(n +169\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(426739084961825187737698778714912406752499606674600864 n^{7}+503918495713490672244899872299963143046199415823723928192 n^{6}+255027256568120470633166791499536261331383645874805068625788 n^{5}+71704385293904477900179758063210564428029632305973175785034165 n^{4}+12096549959152232311599042142758437213254714103592390447178412666 n^{3}+1224430483971012762742075876051581593971019159601096234131715223963 n^{2}+68855701479250899619730272322608655877393650499859399452144523514442 n +1659490153351635502892084954268254355831788720345567445898599531385560\right) a \! \left(n +170\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(74285956168453676383847771019306958716504386431903192 n^{7}+88260574655696068384555167658236948721469819952695944976 n^{6}+44942328091569775158189420708490123717348284157670969352526 n^{5}+12713863692275510316096027326493249156779477124572952922824845 n^{4}+2158025485780610139940464685879404205077460503239203628031350848 n^{3}+219782307494261768292468768082402152855407664433813392036575836199 n^{2}+12435475084788750853572335875758626193864024845931725600547854110854 n +301551404791309224348452730016260885713535465488014742762626743408600\right) a \! \left(n +171\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(12636742425045515173429279411636055455737434598485768 n^{7}+15105900617369843390453403838981599583669488360017132424 n^{6}+7739039044523286277051519576057013290407522422345540120810 n^{5}+2202727407771081074765418809170676896467811180676902176857505 n^{4}+376176473120491303802630524228538285764009479771873962844163172 n^{3}+38546039322121054979406343717632880002373139718056465553463892511 n^{2}+2194327709799497069873894711177847886784615603566599961834274915610 n +53536827235528125488609667196042607211034523468072321523870994969560\right) a \! \left(n +172\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(6392117237813444940325195142160578232862198481720978615900 n^{7}+7320840377658671258809667211270242123959028313443511500931360 n^{6}+3593375371931590343402390030848733778520564204510488020924038463 n^{5}+979882650468842816945362043101130574230771968688722543818055490010 n^{4}+160324260810736848855132905389542892132718651202557699213104626807785 n^{3}+15739039698356157671039682228386718763041041510215269519554393330271390 n^{2}+858395390651038561458591398993036431596114159922564903774685423513852832 n +20064230833615415505222697312991333641373956159431704441383942121169463320\right) a \! \left(n +165\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(2536455729760473890910328625928408483753709738697649445448 n^{7}+2922723594737195639678809567487950475985536570546372539943744 n^{6}+1443358450156786795411559766472864069496492310591653803007467739 n^{5}+395996220974644310956828080336061936914127030066397193117218746640 n^{4}+65187172286716090830740615510997192794336575885723187051511612345317 n^{3}+6438543250579960600205543109398557967466211069057774758507344662803476 n^{2}+353300153857006600481934073485836321190193400744180432018871663230806476 n +8308576181288832667086703112504502294067097514518583348237452748691384920\right) a \! \left(n +166\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(23284763837560585964884333932506022831185512688311077696 n^{7}+26994988126706847985529938897376537164049215705563787457224 n^{6}+13412849860277520071539672971273032959552959017160159524880456 n^{5}+3702456825532078342108136023207693994517455066437475058065061555 n^{4}+613216502359670076122560637287749229714745991704840626553713105454 n^{3}+60938628367104870040308878171169731988817903703580455433682270604321 n^{2}+3364363325169238408440094613906028321548082845033426708085986752295614 n +79604995095315202277784315232339905280749474208496740001240033217464640\right) a \! \left(n +167\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(13101667487616104660524330765647797534982245363249749996 n^{7}+15282542904240307008747527240574383228252727834221539883424 n^{6}+7639975178379465085689173759934557414400213526639893735040252 n^{5}+2121875726617675031878510868827615636682281743226105723362115605 n^{4}+353592863136769128705742492533064294198975978411137066640870753654 n^{3}+35354337738367576231927769942230950195610609121965369390687513152531 n^{2}+1963875524263744807452811841940116645630681326225422882110721962779218 n +46753387796399966332103710415459923199838660248843361262311545060087520\right) a \! \left(n +168\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(296664146606978008070968351396771521383603939691840780687908 n^{7}+335665044779467074131192675929758172463745101452721022268379152 n^{6}+162769047998189386062181852746097937195110520079267569946213781502 n^{5}+43849693013491550984639103804949304660383005340906955175659635546195 n^{4}+7087844343451127984720549501223200385816937405013303679014371217380172 n^{3}+687408286899244462836484931474067370370195434849738990428148912159717393 n^{2}+37037756810846831967122407032248261658798849268286231793927572639162492598 n +855263084762073917786358252788118748110470761819998226797009005485149457320\right) a \! \left(n +163\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(8934134027174889736554332335935203422896308402424968265928 n^{7}+10170201690516786381812393804890437265458613581602921095841392 n^{6}+4961713228046720523895714977842728941500685097779941433654963505 n^{5}+1344816806966552926982094418478349911919105981753463966600687174765 n^{4}+218699519751558917721485032227310230545516243829208727815679811399217 n^{3}+21339579991288590315454460797477059378156708501657920742138471340714243 n^{2}+1156787510297644984260399141468145328236305985860129232903958273666885670 n +26874898030816950318714259503711359681303032619887698043716361363992644640\right) a \! \left(n +164\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(26179101012741833634593836237300015003980069731054370866886980 n^{7}+29085886201648371495913739621651453131786036424334739967715660184 n^{6}+13849501704583748798815139216460217006118854700632908769300639351322 n^{5}+3663655515098293968569104642849592090420021707149848490982405140456325 n^{4}+581497143685803070623003613713752478271534580334093815256304230584045960 n^{3}+55377467704318667276581421544665579824771302278855399779358801120609215831 n^{2}+2929864103333276488157772756909950823510765431294495381879942740140561757398 n +66433409227338542601965188323861433721283167753566207337261329854992534058000\right) a \! \left(n +160\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(6071968867534127200472559173846943461161947749147454442417284 n^{7}+6787317361060489757900155999137760935014698431953962237461069064 n^{6}+3251554803219487724291547586583256328551227954185599586426497984783 n^{5}+865391582609617718838919818329256290972955602395152598669502854312375 n^{4}+138193228326296573018214389886910234327684265905798877756309008270697031 n^{3}+13240776398635197494016052908668807956795477912526038680815784119947751941 n^{2}+704805143253694393154187592146623378458942818602304693530148513116553505362 n +16078643585750944836954648607825293803582667641299307829066422796598808334960\right) a \! \left(n +161\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1363720914418590731047181894679602688005395394152921669048148 n^{7}+1533667423419495397218091425492606353096978743069422114682330136 n^{6}+739198893450407338439105007591503760675670364116564836437159037443 n^{5}+197933916150058857442860534363599565713839391965160775653361212168540 n^{4}+31800340261238403457239480881724493984908208179273534768371102546455397 n^{3}+3065462786761341946938293355831540324956820229211160208155016447193156984 n^{2}+164168336738194793805523714576823747425394993759060937989559385829639536272 n +3767971669130791844596390961067125594205334523397462857775438068814259014240\right) a \! \left(n +162\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(3275750523226241369861685061222573744230903273604425900211381492 n^{7}+3551370237179437576213316609972931447365786139901657359252239932644 n^{6}+1650083734334096071932125383501609417490862565807520932118132801521645 n^{5}+425936895869844522734314730669235521169087248428323022172115106662434730 n^{4}+65968651373808738002029513743462063830805012694042308381844161905508741403 n^{3}+6130319090138577263717092709969295853459850581946235822065122702857433631286 n^{2}+316488545066569873924171882489213659237945302739721707432712938806090377758600 n +7002580923301533966975455018654780967379841421817912163054544102470986342575120\right) a \! \left(n +156\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(864261455916754229689308135030583367827450113078911439086727230 n^{7}+942770530024994115998290957519760355514807942741093706015621721964 n^{6}+440749175789017951158445998456282942947439500083013603492097987020327 n^{5}+114473780034699906677490771977686557233378019134436646979351760158020195 n^{4}+17839117543934396613504371313568888200674988006476865686574280494682460015 n^{3}+1667990630469018934492140457283483013090752543643777577289162061864495361291 n^{2}+86644910158343777131542301409681227669422422404839093523294150964983316361378 n +1928934596499519603049092121019791115581591089940128737892470743465928121621720\right) a \! \left(n +157\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(63096653237641461348849314133296397394289690509475784745338220 n^{7}+69251914258326912481825195316875633828752266855708864687081334576 n^{6}+32574796091397460689108840235733850049755426384236652910847719903195 n^{5}+8512565079794429691301325234913308338726182271194204485189131064347740 n^{4}+1334725100531319825117269094716582701242804260414569302170771275389336865 n^{3}+125567117731486418390326723359537094130091510180234581816779892861163850764 n^{2}+6562798274195071694303695105949524119841257109070300456202238439390688557160 n +147003274574319146562306426838840694574161594158354489492779150514020235121040\right) a \! \left(n +158\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(109281370780570127232153306598939811272299542042855498055049072 n^{7}+120677583966870525102037078482323229768044604858396529969289921944 n^{6}+57112531885569394250902466895786370822157131632194346156207692696200 n^{5}+15016368240776600821469383527968746961064091863335565368763928658913625 n^{4}+2368922902733227535075451078413829682350167819387229421730225521290128938 n^{3}+224227843611188983400547733189832980847507031941326425955893752616003272791 n^{2}+11791174634805128915213284807748273599762266976096367015887254513738232531710 n +265735341294161394684397202752210683260199397487045370264899911354564439675880\right) a \! \left(n +159\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3205571953726729539612490446806790549089261959441313266089917575592 n^{7}+3368180067188650873285187770323735081710489238400144733023192872911664 n^{6}+1516742252690405772403273227764378702100660411092352344066804055516475829 n^{5}+379454155279225757514485596352726398747682741086499885082213759137545029630 n^{4}+56958912804624085777498298924434395807168276193214199800161927161081442514423 n^{3}+5130018967432753911153171684380031420906113129337855431910393937302460401071586 n^{2}+256689111929583298801366159309647948539424030644059673526727879904035018350872556 n +5504563568868519212514160448317411173684713650656686171216536026316980785181203040\right) a \! \left(n +151\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(141085885403122984761989058961381476127994212346291903705678088008 n^{7}+149185382691339494106283685650442922136034870659312287579118625032144 n^{6}+67607558969196444746435133039632265357229257415793368918433271307295789 n^{5}+17021383269941101361815858437397913806241210452967740485781151493386959765 n^{4}+2571277013931507168169059182445244788122666613779907431052106235681754868217 n^{3}+233054428127202979128853246209959171603050465845554476706970544476033001724731 n^{2}+11735365596027310917346571119604385082693116282193886445801420409457429388429546 n +253257569670996233549128457523728475852147173445093547661092547328469564088564400\right) a \! \left(n +152\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(295230140845034324515215237128652840563929843998425664231934741352 n^{7}+314150535601316949891258664815611459533188761867453109548862661925848 n^{6}+143265228145138218250209458111405188583839641852863202690183005799845699 n^{5}+36297273502782423161564156977774140147673517395668195848750328633799747240 n^{4}+5517740107289763092492461125326546275216567766834514747188805179607915455273 n^{3}+503271761201336423113296966393736226541000411697958274403161724193162781385192 n^{2}+25502001685799165815722973171196815227017372068067587190371647977691743883653676 n +553824468306432398346119314403034305173962684290660553090272665884591408926947560\right) a \! \left(n +153\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(85592012121935313727138680750820801334598782152216880985916537412 n^{7}+91649035275926470922119900687325060226031467923641847483424034544448 n^{6}+42057947724029194829846830585252859897761901102258934031334290990428398 n^{5}+10722550794931333013809485579294334075408284468318763997433601084864904145 n^{4}+1640218924567008759918745415041277923790505824510687633704635295465542058268 n^{3}+150542545179623883896574702017033582847145224777736922811295639608591619758747 n^{2}+7676207807449956553899559143114613804575489532386965894994883147402920682962582 n +167749024871046942538988137299988023760835510274714462499805552848541824406529600\right) a \! \left(n +154\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(24055478185638181124767864363982265081142323525898220825813575272 n^{7}+25918559374677062740425488809071701398484895831995988497833469866336 n^{6}+11968312279389341198731118242379852961495407134201374724118878344120471 n^{5}+3070326051576904911201197681770412980257228106313087209502723461743767725 n^{4}+472595336182833569042546961583174633213721043856256661157880908689062352843 n^{3}+43646334409330223487175927938081223753649562335252613595564479176123991027619 n^{2}+2239421466958139210762663506680257895921509945934957620684518756706423892643734 n +49243554860739676716334988111769891488432137956247165295562783034020807142699920\right) a \! \left(n +155\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(10101112086929866459586936513314016292334913571180660947612333168612 n^{7}+10545947066864224352910904692890107905989878503095273463173232581559888 n^{6}+4718773924544631553574726141629297992861120659250105994600526958320781881 n^{5}+1173016903846304959438613642355328965271708587178916713973693405792082243045 n^{4}+174958356517840702940443117036826138682171737836138121976633762404880717165293 n^{3}+15657430009613653523610765477871612155832543059407578741300021717672137657540447 n^{2}+778462916634857018146516989375557375769984348187386178523349719718400635295621674 n +16587571520827307548033962326111448093413105074638979403806780774440914121455364120\right) a \! \left(n +150\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(133182122713159099806242698692767633036826309522777378934159167512672 n^{7}+136362540954101277073744268512819565205927715215058735286662524338889724 n^{6}+59837464298687974054319067552834908412248876342535049329105326051259557492 n^{5}+14587623411509523964786521282499885879934036572671471497834325411844272085255 n^{4}+2133796348753148282679675141206536017432447171905847280224812326035069362181518 n^{3}+187274435106380568786574412744111869965869303817668211761025787829146116595267531 n^{2}+9131400949848203126257209373886643821671356758168969181950592437215523272160752968 n +190820697153012121267997547663935212865992264400669241339014699248354239878343184680\right) a \! \left(n +147\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(3286006624899124979554038204150333273685826582062329115103540496541 n^{7}+3386627261968277855380760874026000581596466810941786581910529084856054 n^{6}+1495872768643650882136788972425284034248237507438817440299337153830482131 n^{5}+367074763312637891043514360650929673197655578902644893954721778809118120850 n^{4}+54046903001246477558683194919380526116786366451251045235976423339060720669809 n^{3}+4774672151126129155395205627525338887308800003535925029773220637116745200023716 n^{2}+234341413608953868949730132113346266144748322196268760746718487300403340907172799 n +4929274937965911779786955381244282567819986763426975494399335384719370055600185640\right) a \! \left(n +148\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(10306700725966344832595764319923577279841400929264278710906528909756 n^{7}+10691533660623520004398177437285480422037220668484344667542057527365608 n^{6}+4753221567625550655388938204874039560079200303137703645465544447479326937 n^{5}+1174000134770195864969605589615657077136519063711953035114946019811787376070 n^{4}+173981901257076486319324685520997799102164557417227414131195377555718855472139 n^{3}+15470198353338214174986519653286468052232676851345604195686356405164146734011522 n^{2}+764222580920505163108631271991749028592818907156220730484825042256516534712876808 n +16179749335219468262631795903000751746148037957843401507073562319979130295763907600\right) a \! \left(n +149\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(2072890081332511602421571978794491605808630027260950709152953755448504 n^{7}+2065674529561506303316057120175611232659552278958855648082094342332228992 n^{6}+882226408077423854564874063278024848483487732734474277176472958344230040331 n^{5}+209331733064667708142551860515938421594290918131459523533647173729042523356460 n^{4}+29802365297455542387151329377657253208465929387878210569488735107288664637290921 n^{3}+2545816424916479505783381134503761682618249843942227625341540238176774771754604668 n^{2}+120820436447195262592845448481894417746374005521662586295659346653453972817297754204 n +2457459880310155848622450184205204798325254009836843699402936440081853638576165842360\right) a \! \left(n +143\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(5535161922554165804154540057412686071172859879843252214789890291554584 n^{7}+5554187757397807009409165708983018486043568970818113799042663619688030184 n^{6}+2388593564298501465556565723387336791594433206315789479196977150249178272050 n^{5}+570689327395428929870852623144055998654202798688668100880168298753968834885215 n^{4}+81811965773105938968241814430478937745113128471256996441438961859198918831931156 n^{3}+7037096807224802775234870938134343787543700740138092968876134489987351506870070681 n^{2}+336283936970199571092343459970888687984966243740230257385093748927332085310891367330 n +6887321800526580782710756031413646856826846992959324491137578552985509763372312439800\right) a \! \left(n +144\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(2063640252010786079973584115241933613979599881306649113473007880745668 n^{7}+2084890018348897485677145372177017720867287563761472215945421655458197064 n^{6}+902740304425079975714353120123575692420233963537955196920773659479147255990 n^{5}+217158761799042744493704127467541903558347200253423549464211977580590655809805 n^{4}+31343718283341454168974680827494286221235472281936386237830146654129097622673232 n^{3}+2714453118504896144427166471101332023463635388895047954937620946125136011912174211 n^{2}+130601789571672925436734333953240699066241560230203642956294028141130880944596122990 n +2693063653306175106061044274035780418739469475369231554377943169912220386152476924280\right) a \! \left(n +145\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(750915956395753555545261078459846685930138179706256656322206016857444 n^{7}+763762976118356162698218558165776100397037997969284488171258352198987984 n^{6}+332932010712646606790202739084148796591578717719735064725906991389102351933 n^{5}+80628115330162079318579597380724264772249333520792125465209523048601942946255 n^{4}+11715889333475079872423378533152882594184703741996812429255128823894391591008621 n^{3}+1021461141176611589537564076306090039613615967535389005811387568188442081026551781 n^{2}+49476908782502603240410305339583829861676630484319880645879780744890209482687596502 n +1027100978957037229382663202891162723381467641528878130032851462453952301216721312040\right) a \! \left(n +146\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(31222524727031177516936307955510233671699599500393746019375975518023984 n^{7}+30675312801861295913138458254713455135255710262655497236148940622385814016 n^{6}+12916501566504894914568188961474523865016602368481062919565102724052029624991 n^{5}+3021621406370653207488991885602433436135156002700911024894579270233055386776215 n^{4}+424129269186066939252117780725482342399697642535576905462355279632054969381683531 n^{3}+35720664756457139214882687024948133102628401858884912123063963903033646987607339609 n^{2}+1671399242856854489623791124884982412668409706601530303485395803301985537273652618734 n +33517839098164394362195781899297655270355144908095178915457011687689025021800486461360\right) a \! \left(n +141\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(18616325918770980594235817321863254021123958009183138986691092439229092 n^{7}+18421481774685120116252288754105870344535348633693501427248989883015752400 n^{6}+7812478714112474104354236043098195259140136530859033134968199899162697451309 n^{5}+1840734507636689476585249997361438104626874286417970519175898795994268559146850 n^{4}+260228750829534491814499665387043300510872037343044870253758816993028922333165463 n^{3}+22074011024120785915559608995993282079563853181972698462293402634639450661929697610 n^{2}+1040268314776968534024652225858415758115796157275451528341959350520127635413810935156 n +21010838283625724034759056055087082622565198249690451104797391209648070974580777877500\right) a \! \left(n +142\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(673526453391028117877013446546980300537738796511409800899213922596932414 n^{7}+647145073696872615755012449260565438342252793207269581796667459196059832096 n^{6}+266493574589349811005274602247862426773489949096319494675241899091370382951560 n^{5}+60969735136422832030228349504777540924157506900886786878375149760571886147511625 n^{4}+8369667280072947688991823858642868807047648849805437535049117806712561931571884286 n^{3}+689395567913454157801531937429433934901935710031814235408196357217551313010215883459 n^{2}+31547977262150733793901951578707678737604210672511547196682205334414928601318534526300 n +618746983365533808394282012611487443532789591877200212577488304663901747727545325079380\right) a \! \left(n +138\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(562489706945430723445082001887171692367157577762899161485394575072287056 n^{7}+544556869072883251174298854244841429854163209088962231508561816564068754416 n^{6}+225948328269474981582586215682999867237621061168969605202909682947665509299975 n^{5}+52085472441608113930989936435502788669351447440697864252143426567812937890548800 n^{4}+7204261904688967293200316879718398509612307750862088957510904967032221402475857309 n^{3}+597899040589055924665728264407314141735910822840382426704788146567966650054025726704 n^{2}+27568174593269834484649048972824266018782833521507174015390315971599037929301635795420 n +544785751129792461789087824534809686330113419003060031872134227738983739703541584741360\right) a \! \left(n +139\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(231424262183343368508118986329468040990417521945586489474296201664583904 n^{7}+225716254788293257798081194078711309259825017513840342072603701901865462688 n^{6}+94352391583777935767381003400138053267724147605935013945642980706997015481358 n^{5}+21912072552875488885001169100991006762932491714685545540427660377042241253060225 n^{4}+3053361885802521846108425940583903720552091328661203226462311572133521568212506676 n^{3}+255292135302040445855948709700798924677620446037437035733408773301073117198119198967 n^{2}+11858703801089444243977124851292335678088504866097238848085273592565498803899626174502 n +236087725737362541987790384097746989604712016315682215743087169473098154644148595986880\right) a \! \left(n +140\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3182667344644018335885936856390564809899582475954068439472079138209022072 n^{7}+3034625611000835334401318442838849433737702116551646257639564920660907424616 n^{6}+1240102552344184661069908772781801521065241635849421176664551754007175636779137 n^{5}+281548418304218547176410955437816311969765436164867000960444515365465195793442115 n^{4}+38354423542837324333214022272171612455747484432589422440252683396030885754155938513 n^{3}+3135052493832644285851888670085538128068031950349842586067711794624046790769082603729 n^{2}+142369683145938975424106033505735229879887411953505053214250617537914700276098929391298 n +2770954482352189700339252473698050099024689760626612264519446613862489555986625684840400\right) a \! \left(n +137\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}, \quad n \geq 206$$
Heatmap

To create this heatmap, we sampled 1,000,000 permutations of length 300 uniformly at random. The color of the point $$(i, j)$$ represents how many permutations have value $$j$$ at index $$i$$ (darker = more).

### This specification was found using the strategy pack "Point Placements" and has 551 rules.

Found on January 17, 2022.

Finding the specification took 162252 seconds.

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\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{28}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{28}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{515}\! \left(x \right)+F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{0} \left(x \right)^{2}\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{479}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x \right)\\ F_{15}\! \left(x \right) &= -F_{30}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= \frac{F_{17}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{27}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{28}\! \left(x \right) &= x\\ F_{29}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{28}\! \left(x \right) F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{28}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{477}\! \left(x \right)\\ F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= -F_{187}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{0}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{28}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{28}\! \left(x \right) F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49} \left(x \right)^{2}\\ F_{49}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{28}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{49} \left(x \right)^{2} F_{28}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)\\ F_{58}\! \left(x \right) &= 0\\ F_{59}\! \left(x \right) &= F_{28}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{28}\! \left(x \right) F_{56}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{64}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{28}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{28}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{50}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{28}\! \left(x \right) F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{449}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{2}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{28}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{447}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{446}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= \frac{F_{80}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{28}\! \left(x \right) F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{2}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{86}\! \left(x \right) &= -F_{445}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{87}\! \left(x \right) &= -F_{99}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= \frac{F_{89}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{28}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{2}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{95}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= \frac{F_{97}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{97}\! \left(x \right) &= F_{25}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{0}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{0}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{101}\! \left(x \right) &= -F_{102}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{102}\! \left(x \right) &= -F_{105}\! \left(x \right)+F_{103}\! \left(x \right)\\ F_{103}\! \left(x \right) &= \frac{F_{104}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{104}\! \left(x \right) &= F_{90}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{430}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{0}\! \left(x \right) F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{425}\! \left(x \right)\\ F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{117}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{125}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{123}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{124}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{398}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{253}\! \left(x \right)\\ F_{129}\! \left(x \right) &= \frac{F_{130}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{133}\! \left(x \right) &= \frac{F_{134}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{142}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{50}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{144}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{149}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{146}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{145}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{149}\! \left(x \right) &= -F_{150}\! \left(x \right)+F_{133}\! \left(x \right)\\ F_{150}\! \left(x \right) &= \frac{F_{151}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{154}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{0}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{156}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)+F_{248}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{160}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{160}\! \left(x \right) &= \frac{F_{161}\! \left(x \right)}{F_{50}\! \left(x \right)}\\ F_{161}\! \left(x \right) &= -F_{166}\! \left(x \right)+F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= \frac{F_{163}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= -F_{165}\! \left(x \right)+F_{131}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{4}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{168}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{168}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{169}\! \left(x \right)\\ F_{169}\! \left(x \right) &= \frac{F_{170}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{172}\! \left(x \right) &= -F_{179}\! \left(x \right)+F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= \frac{F_{174}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= -F_{178}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{176}\! \left(x \right) &= \frac{F_{177}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{177}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{181}\! \left(x \right) &= -F_{182}\! \left(x \right)+F_{173}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= \frac{F_{184}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\ F_{185}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{188}\! \left(x \right) &= -F_{237}\! \left(x \right)+F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= \frac{F_{190}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{193}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{193}\! \left(x \right) &= \frac{F_{194}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= -F_{236}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{199}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{226}\! \left(x \right)\\ F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{202}\! \left(x \right)\\ F_{201}\! \left(x \right) &= F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{204}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{205}\! \left(x \right)\\ F_{205}\! \left(x \right) &= \frac{F_{206}\! \left(x \right)}{F_{49}\! \left(x \right)}\\ F_{206}\! \left(x \right) &= -F_{207}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{207}\! \left(x \right) &= \frac{F_{208}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{208}\! \left(x \right) &= F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= -F_{225}\! \left(x \right)+F_{210}\! \left(x \right)\\ F_{210}\! \left(x \right) &= -F_{212}\! \left(x \right)+F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{212}\! \left(x \right) &= -F_{223}\! \left(x \right)+F_{213}\! \left(x \right)\\ F_{213}\! \left(x \right) &= -F_{217}\! \left(x \right)+F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= \frac{F_{215}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\ F_{216}\! \left(x \right) &= -F_{41}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{220}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= F_{159}\! \left(x \right) F_{222}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{224}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{0}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{228}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{230}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{200}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right) F_{49}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{235}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{232}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{201}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{240}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{239}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{240}\! \left(x \right) &= -F_{241}\! \left(x \right)+F_{189}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{244}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{243}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{213}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{245}\! \left(x \right) &= \frac{F_{246}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}\\ F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{205}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{251}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{149}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{129}\! \left(x \right) F_{255}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{256}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)\\ F_{257}\! \left(x \right) &= F_{258}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{258}\! \left(x \right) &= \frac{F_{259}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)\\ F_{260}\! \left(x \right) &= -F_{397}\! \left(x \right)+F_{261}\! \left(x \right)\\ F_{261}\! \left(x \right) &= \frac{F_{262}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{262}\! \left(x \right) &= F_{263}\! \left(x \right)\\ F_{263}\! \left(x \right) &= \frac{F_{264}\! \left(x \right)}{F_{11}\! \left(x \right) F_{49}\! \left(x \right)}\\ F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= -F_{346}\! \left(x \right)+F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= -F_{339}\! \left(x \right)+F_{267}\! \left(x \right)\\ F_{267}\! \left(x \right) &= \frac{F_{268}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= -F_{272}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= \frac{F_{271}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{271}\! \left(x \right) &= F_{90}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= -F_{274}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{277}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{277}\! \left(x \right) &= \frac{F_{278}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{278}\! \left(x \right) &= F_{279}\! \left(x \right)\\ F_{279}\! \left(x \right) &= -F_{280}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{280}\! \left(x \right) &= \frac{F_{281}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}\\ F_{281}\! \left(x \right) &= F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= \frac{F_{283}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{283}\! \left(x \right) &= F_{284}\! \left(x \right)\\ F_{284}\! \left(x \right) &= -F_{285}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{285}\! \left(x \right) &= -F_{338}\! \left(x \right)+F_{286}\! \left(x \right)\\ F_{286}\! \left(x \right) &= -F_{287}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{287}\! \left(x \right) &= F_{288}\! \left(x \right)\\ F_{288}\! \left(x \right) &= F_{0}\! \left(x \right) F_{289}\! \left(x \right)\\ F_{289}\! \left(x \right) &= \frac{F_{290}\! \left(x \right)}{F_{50}\! \left(x \right)}\\ F_{290}\! \left(x \right) &= -F_{26}\! \left(x \right)+F_{291}\! \left(x \right)\\ F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)+F_{295}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{28}\! \left(x \right) F_{49}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{295}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{296}\! \left(x \right)\\ F_{296}\! \left(x \right) &= -F_{319}\! \left(x \right)+F_{297}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{28}\! \left(x \right) F_{299}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{300}\! \left(x \right)+F_{308}\! \left(x \right)\\ F_{300}\! \left(x \right) &= -F_{13}\! \left(x \right)+F_{301}\! \left(x \right)\\ F_{301}\! \left(x \right) &= -F_{304}\! \left(x \right)+F_{302}\! \left(x \right)\\ F_{302}\! \left(x \right) &= \frac{F_{303}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{303}\! \left(x \right) &= F_{10}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{305}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{28}\! \left(x \right) F_{306}\! \left(x \right)\\ F_{306}\! \left(x \right) &= \frac{F_{307}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{307}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{308}\! \left(x \right) &= F_{309}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{28}\! \left(x \right) F_{310}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{311}\! \left(x \right)+F_{315}\! \left(x \right)\\ F_{311}\! \left(x \right) &= F_{26}\! \left(x \right) F_{312}\! \left(x \right)\\ F_{312}\! \left(x \right) &= -F_{13}\! \left(x \right)+F_{313}\! \left(x \right)\\ F_{313}\! \left(x \right) &= \frac{F_{314}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{314}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)\\ F_{316}\! \left(x \right) &= F_{317}\! \left(x \right) F_{318}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{317}\! \left(x \right) &= -F_{279}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{318}\! \left(x \right) &= -F_{123}\! \left(x \right)+F_{232}\! \left(x \right)\\ F_{319}\! \left(x \right) &= F_{320}\! \left(x \right)\\ F_{320}\! \left(x \right) &= F_{28}\! \left(x \right) F_{321}\! \left(x \right)\\ F_{321}\! \left(x \right) &= F_{322}\! \left(x \right)+F_{336}\! \left(x \right)\\ F_{322}\! \left(x \right) &= F_{26}\! \left(x \right) F_{323}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{324}\! \left(x \right)\\ F_{324}\! \left(x \right) &= F_{28}\! \left(x \right) F_{325}\! \left(x \right)\\ F_{325}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{326}\! \left(x \right)\\ F_{326}\! \left(x \right) &= F_{323}\! \left(x \right)+F_{327}\! \left(x \right)\\ F_{327}\! \left(x \right) &= F_{328}\! \left(x \right)\\ F_{328}\! \left(x \right) &= F_{28}\! \left(x \right) F_{329}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{329}\! \left(x \right) &= F_{330}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{330}\! \left(x \right) &= F_{331}\! \left(x \right)+F_{332}\! \left(x \right)\\ F_{331}\! \left(x \right) &= F_{153}\! \left(x \right)\\ F_{332}\! \left(x \right) &= F_{333}\! \left(x \right)\\ F_{333}\! \left(x \right) &= F_{28}\! \left(x \right) F_{334}\! \left(x \right)\\ F_{334}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{335}\! \left(x \right)\\ F_{335}\! \left(x \right) &= F_{18}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{336}\! \left(x \right) &= F_{337}\! \left(x \right)\\ F_{337}\! \left(x \right) &= F_{113}\! \left(x \right) F_{317}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{338}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{332}\! \left(x \right)\\ F_{339}\! \left(x \right) &= \frac{F_{340}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{340}\! \left(x \right) &= F_{341}\! \left(x \right)\\ F_{341}\! \left(x \right) &= -F_{26}\! \left(x \right)+F_{342}\! \left(x \right)\\ F_{342}\! \left(x \right) &= -F_{345}\! \left(x \right)+F_{343}\! \left(x \right)\\ F_{343}\! \left(x \right) &= \frac{F_{344}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{344}\! \left(x \right) &= F_{18}\! \left(x \right)\\ F_{345}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{297}\! \left(x \right)\\ F_{346}\! \left(x \right) &= F_{347}\! \left(x \right)+F_{348}\! \left(x \right)\\ F_{347}\! \left(x \right) &= F_{0}\! \left(x \right) F_{273}\! \left(x \right)\\ F_{348}\! \left(x \right) &= F_{349}\! \left(x \right)+F_{351}\! \left(x \right)\\ F_{349}\! \left(x \right) &= F_{350}\! \left(x \right)\\ F_{350}\! \left(x \right) &= F_{266}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{351}\! \left(x \right) &= F_{352}\! \left(x \right)\\ F_{352}\! \left(x \right) &= F_{28}\! \left(x \right) F_{353}\! \left(x \right)\\ F_{353}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{376}\! \left(x \right)\\ F_{354}\! \left(x \right) &= F_{273}\! \left(x \right) F_{355}\! \left(x \right)\\ F_{355}\! \left(x \right) &= F_{356}\! \left(x \right)+F_{372}\! \left(x \right)\\ F_{356}\! \left(x \right) &= F_{357}\! \left(x \right)\\ F_{357}\! \left(x \right) &= F_{28}\! \left(x \right) F_{358}\! \left(x \right)\\ F_{358}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{359}\! \left(x \right) &= F_{360}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{360}\! \left(x \right) &= F_{361}\! \left(x \right)\\ F_{361}\! \left(x \right) &= F_{28}\! \left(x \right) F_{362}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{362}\! \left(x \right) &= F_{359}\! \left(x \right)+F_{363}\! \left(x \right)\\ F_{363}\! \left(x \right) &= -F_{358}\! \left(x \right)+F_{364}\! \left(x \right)\\ F_{364}\! \left(x \right) &= -F_{367}\! \left(x \right)+F_{365}\! \left(x \right)\\ F_{365}\! \left(x \right) &= \frac{F_{366}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{366}\! \left(x \right) &= F_{87}\! \left(x \right)\\ F_{367}\! \left(x \right) &= F_{368}\! \left(x \right)\\ F_{368}\! \left(x \right) &= F_{28}\! \left(x \right) F_{369}\! \left(x \right)\\ F_{369}\! \left(x \right) &= F_{365}\! \left(x \right)+F_{370}\! \left(x \right)\\ F_{370}\! \left(x \right) &= F_{371}\! \left(x \right)\\ F_{371}\! \left(x \right) &= F_{261}\! \left(x \right) F_{50}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{372}\! \left(x \right) &= F_{373}\! \left(x \right)+F_{374}\! \left(x \right)\\ F_{373}\! \left(x \right) &= F_{327}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{374}\! \left(x \right) &= -F_{375}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{375}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{282}\! \left(x \right)\\ F_{376}\! \left(x \right) &= F_{377}\! \left(x \right)\\ F_{377}\! \left(x \right) &= F_{263}\! \left(x \right) F_{378}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{378}\! \left(x \right) &= F_{379}\! \left(x \right)\\ F_{379}\! \left(x \right) &= F_{28}\! \left(x \right) F_{380}\! \left(x \right)\\ F_{380}\! \left(x \right) &= \frac{F_{381}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{381}\! \left(x \right) &= F_{382}\! \left(x \right)\\ F_{382}\! \left(x \right) &= -F_{385}\! \left(x \right)+F_{383}\! \left(x \right)\\ F_{383}\! \left(x \right) &= \frac{F_{384}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{384}\! \left(x \right) &= F_{374}\! \left(x \right)\\ F_{385}\! \left(x \right) &= -F_{388}\! \left(x \right)+F_{386}\! \left(x \right)\\ F_{386}\! \left(x \right) &= \frac{F_{387}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{387}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{388}\! \left(x \right) &= F_{389}\! \left(x \right)\\ F_{389}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{390}\! \left(x \right)\\ F_{390}\! \left(x \right) &= F_{391}\! \left(x \right)+F_{392}\! \left(x \right)\\ F_{391}\! \left(x \right) &= F_{289}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{392}\! \left(x \right) &= F_{393}\! \left(x \right)\\ F_{393}\! \left(x \right) &= F_{28}\! \left(x \right) F_{394}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{394}\! \left(x \right) &= \frac{F_{395}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{395}\! \left(x \right) &= F_{396}\! \left(x \right)\\ F_{396}\! \left(x \right) &= -F_{289}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{397}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{398}\! \left(x \right) &= F_{399}\! \left(x \right)\\ F_{399}\! \left(x \right) &= F_{28}\! \left(x \right) F_{400}\! \left(x \right)\\ F_{400}\! \left(x \right) &= \frac{F_{401}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}\\ F_{401}\! \left(x \right) &= F_{402}\! \left(x \right)\\ F_{402}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{403}\! \left(x \right)\\ F_{403}\! \left(x \right) &= F_{404}\! \left(x \right)\\ F_{404}\! \left(x \right) &= F_{160}\! \left(x \right) F_{28}\! \left(x \right) F_{405}\! \left(x \right)\\ F_{405}\! \left(x \right) &= F_{406}\! \left(x \right)+F_{409}\! \left(x \right)\\ F_{406}\! \left(x \right) &= F_{358}\! \left(x \right)+F_{407}\! \left(x \right)\\ F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)\\ F_{408}\! \left(x \right) &= F_{28}\! \left(x \right) F_{405}\! \left(x \right)\\ F_{409}\! \left(x \right) &= -F_{418}\! \left(x \right)+F_{410}\! \left(x \right)\\ F_{410}\! \left(x \right) &= \frac{F_{411}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{411}\! \left(x \right) &= F_{412}\! \left(x \right)\\ F_{412}\! \left(x \right) &= -F_{417}\! \left(x \right)+F_{413}\! \left(x \right)\\ F_{413}\! \left(x \right) &= \frac{F_{414}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{414}\! \left(x \right) &= F_{415}\! \left(x \right)\\ F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{416}\! \left(x \right) &= F_{44}\! \left(x \right)\\ F_{417}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{260}\! \left(x \right)\\ F_{418}\! \left(x \right) &= \frac{F_{419}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{419}\! \left(x \right) &= F_{420}\! \left(x \right)\\ F_{420}\! \left(x \right) &= -F_{121}\! \left(x \right)+F_{421}\! \left(x \right)\\ F_{421}\! \left(x \right) &= -F_{363}\! \left(x \right)+F_{422}\! \left(x \right)\\ F_{422}\! \left(x \right) &= F_{417}\! \left(x \right)+F_{423}\! \left(x \right)\\ F_{423}\! \left(x \right) &= F_{424}\! \left(x \right)\\ F_{424}\! \left(x \right) &= F_{28}\! \left(x \right) F_{410}\! \left(x \right)\\ F_{425}\! \left(x \right) &= F_{426}\! \left(x \right)\\ F_{426}\! \left(x \right) &= F_{28}\! \left(x \right) F_{427}\! \left(x \right)\\ F_{427}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{428}\! \left(x \right)\\ F_{428}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{429}\! \left(x \right)\\ F_{429}\! \left(x \right) &= F_{113}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{430}\! \left(x \right) &= F_{431}\! \left(x \right)\\ F_{431}\! \left(x \right) &= F_{28}\! \left(x \right) F_{432}\! \left(x \right)\\ F_{432}\! \left(x \right) &= F_{433}\! \left(x \right)+F_{440}\! \left(x \right)\\ F_{433}\! \left(x \right) &= F_{434}\! \left(x \right)\\ F_{434}\! \left(x \right) &= F_{28}\! \left(x \right) F_{364}\! \left(x \right) F_{435}\! \left(x \right)\\ F_{435}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{436}\! \left(x \right)\\ F_{436}\! \left(x \right) &= F_{437}\! \left(x \right)\\ F_{437}\! \left(x \right) &= F_{28}\! \left(x \right) F_{438}\! \left(x \right)\\ F_{438}\! \left(x \right) &= \frac{F_{439}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{439}\! \left(x \right) &= F_{117}\! \left(x \right)\\ F_{440}\! \left(x \right) &= F_{441}\! \left(x \right)\\ F_{441}\! \left(x \right) &= F_{28}\! \left(x \right) F_{442}\! \left(x \right)\\ F_{442}\! \left(x \right) &= F_{432}\! \left(x \right)+F_{443}\! \left(x \right)\\ F_{443}\! \left(x \right) &= F_{444}\! \left(x \right)\\ F_{444}\! \left(x \right) &= F_{142}\! \left(x \right) F_{261}\! \left(x \right)\\ F_{445}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{446}\! \left(x \right) &= F_{2}\! \left(x \right) F_{50}\! \left(x \right) F_{55}\! \left(x \right)\\ F_{447}\! \left(x \right) &= F_{448}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{448}\! \left(x \right) &= F_{360}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{449}\! \left(x \right) &= F_{450}\! \left(x \right)+F_{451}\! \left(x \right)\\ F_{450}\! \left(x \right) &= F_{122}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{451}\! \left(x \right) &= F_{452}\! \left(x \right)\\ F_{452}\! \left(x \right) &= F_{28}\! \left(x \right) F_{453}\! \left(x \right)\\ F_{453}\! \left(x \right) &= F_{454}\! \left(x \right)+F_{466}\! \left(x \right)\\ F_{454}\! \left(x \right) &= F_{455}\! \left(x \right)+F_{456}\! \left(x \right)\\ F_{455}\! \left(x \right) &= F_{2}\! \left(x \right) F_{359}\! \left(x \right)\\ F_{456}\! \left(x \right) &= F_{457}\! \left(x \right)\\ F_{457}\! \left(x \right) &= F_{28}\! \left(x \right) F_{458}\! \left(x \right)\\ F_{458}\! \left(x \right) &= F_{453}\! \left(x \right)+F_{459}\! \left(x \right)\\ F_{459}\! \left(x \right) &= F_{460}\! \left(x \right)\\ F_{460}\! \left(x \right) &= F_{461}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{461}\! \left(x \right) &= F_{462}\! \left(x \right)+F_{464}\! \left(x \right)\\ F_{462}\! \left(x \right) &= F_{463}\! \left(x \right)\\ F_{463}\! \left(x \right) &= F_{146}\! \left(x \right) F_{255}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{464}\! \left(x \right) &= F_{465}\! \left(x \right)\\ F_{465}\! \left(x \right) &= F_{212}\! \left(x \right) F_{255}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{466}\! \left(x \right) &= F_{467}\! \left(x \right)+F_{468}\! \left(x \right)\\ F_{467}\! \left(x \right) &= F_{18}\! \left(x \right) F_{359}\! \left(x \right)\\ F_{468}\! \left(x \right) &= F_{469}\! \left(x \right)\\ F_{469}\! \left(x \right) &= F_{28}\! \left(x \right) F_{470}\! \left(x \right)\\ F_{470}\! \left(x \right) &= F_{471}\! \left(x \right)+F_{472}\! \left(x \right)\\ F_{471}\! \left(x \right) &= F_{172}\! \left(x \right) F_{359}\! \left(x \right)\\ F_{472}\! \left(x \right) &= F_{473}\! \left(x \right)\\ F_{473}\! \left(x \right) &= F_{474}\! \left(x \right) F_{476}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{474}\! \left(x \right) &= F_{475}\! \left(x \right)\\ F_{475}\! \left(x \right) &= F_{255}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{476}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{205}\! \left(x \right)\\ F_{477}\! \left(x \right) &= F_{478}\! \left(x \right)\\ F_{478}\! \left(x \right) &= F_{228}\! \left(x \right) F_{28}\! \left(x \right)\\ F_{479}\! \left(x \right) &= F_{480}\! \left(x \right)\\ F_{480}\! \left(x \right) &= F_{28}\! \left(x \right) F_{481}\! \left(x \right)\\ F_{481}\! \left(x \right) &= F_{482}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{482}\! \left(x \right) &= F_{483}\! \left(x \right)+F_{488}\! \left(x \right)\\ F_{483}\! \left(x \right) &= F_{484}\! \left(x \right)\\ F_{484}\! \left(x \right) &= F_{0}\! \left(x \right) F_{485}\! \left(x \right)\\ F_{485}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{486}\! \left(x \right)\\ F_{486}\! \left(x \right) &= F_{487}\! \left(x \right)\\ F_{487}\! \left(x \right) &= F_{123}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{488}\! \left(x \right) &= F_{489}\! \left(x \right)\\ F_{489}\! \left(x \right) &= F_{28}\! \left(x \right) F_{490}\! \left(x \right)\\ F_{490}\! \left(x \right) &= F_{491}\! \left(x \right)+F_{508}\! \left(x \right)\\ F_{491}\! \left(x \right) &= -F_{498}\! \left(x \right)+F_{492}\! \left(x \right)\\ F_{492}\! \left(x \right) &= \frac{F_{493}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{493}\! \left(x \right) &= F_{494}\! \left(x \right)\\ F_{494}\! \left(x \right) &= -F_{495}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{495}\! \left(x \right) &= F_{496}\! \left(x \right)\\ F_{496}\! \left(x \right) &= F_{0}\! \left(x \right) F_{497}\! \left(x \right)\\ F_{497}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{498}\! \left(x \right) &= F_{499}\! \left(x \right)+F_{507}\! \left(x \right)\\ F_{499}\! \left(x \right) &= F_{500}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{500}\! \left(x \right) &= F_{501}\! \left(x \right)\\ F_{501}\! \left(x \right) &= F_{28}\! \left(x \right) F_{502}\! \left(x \right)\\ F_{502}\! \left(x \right) &= \frac{F_{503}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{503}\! \left(x \right) &= F_{504}\! \left(x \right)\\ F_{504}\! \left(x \right) &= F_{351}\! \left(x \right)+F_{505}\! \left(x \right)\\ F_{505}\! \left(x \right) &= -F_{341}\! \left(x \right)+F_{506}\! \left(x \right)\\ F_{506}\! \left(x \right) &= -F_{96}\! \left(x \right)+F_{339}\! \left(x \right)\\ F_{507}\! \left(x \right) &= F_{2}\! \left(x \right) F_{273}\! \left(x \right)\\ F_{508}\! \left(x \right) &= F_{509}\! \left(x \right)\\ F_{509}\! \left(x \right) &= F_{123}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right) F_{510}\! \left(x \right)\\ F_{510}\! \left(x \right) &= \frac{F_{511}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}\\ F_{511}\! \left(x \right) &= F_{512}\! \left(x \right)\\ F_{512}\! \left(x \right) &= -F_{513}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{513}\! \left(x \right) &= F_{514}\! \left(x \right)\\ F_{514}\! \left(x \right) &= F_{0}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{515}\! \left(x \right) &= F_{516}\! \left(x \right)+F_{518}\! \left(x \right)\\ F_{516}\! \left(x \right) &= F_{517}\! \left(x \right)\\ F_{517}\! \left(x \right) &= F_{2}\! \left(x \right) F_{289}\! \left(x \right)\\ F_{518}\! \left(x \right) &= F_{519}\! \left(x \right)\\ F_{519}\! \left(x \right) &= F_{28}\! \left(x \right) F_{520}\! \left(x \right)\\ F_{520}\! \left(x \right) &= F_{521}\! \left(x \right)+F_{522}\! \left(x \right)\\ F_{521}\! \left(x \right) &= F_{289}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{522}\! \left(x \right) &= F_{523}\! \left(x \right)+F_{530}\! \left(x \right)\\ F_{523}\! \left(x \right) &= F_{524}\! \left(x \right)+F_{529}\! \left(x \right)\\ F_{524}\! \left(x \right) &= F_{515}\! \left(x \right)+F_{525}\! \left(x \right)\\ F_{525}\! \left(x \right) &= F_{526}\! \left(x \right)+F_{527}\! \left(x \right)\\ F_{526}\! \left(x \right) &= F_{356}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{527}\! \left(x \right) &= F_{528}\! \left(x \right)\\ F_{528}\! \left(x \right) &= F_{28}\! \left(x \right) F_{312}\! \left(x \right) F_{397}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{529}\! \left(x \right) &= F_{289}\! \left(x \right) F_{323}\! \left(x \right)\\ F_{530}\! \left(x \right) &= -F_{524}\! \left(x \right)+F_{531}\! \left(x \right)\\ F_{531}\! \left(x \right) &= F_{532}\! \left(x \right)+F_{541}\! \left(x \right)\\ F_{532}\! \left(x \right) &= -F_{536}\! \left(x \right)+F_{533}\! \left(x \right)\\ F_{533}\! \left(x \right) &= \frac{F_{534}\! \left(x \right)}{F_{28}\! \left(x \right)}\\ F_{534}\! \left(x \right) &= F_{535}\! \left(x \right)\\ F_{535}\! \left(x \right) &= -F_{4}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{536}\! \left(x \right) &= F_{537}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{537}\! \left(x \right) &= F_{538}\! \left(x \right)+F_{539}\! \left(x \right)\\ F_{538}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{539}\! \left(x \right) &= F_{540}\! \left(x \right)\\ F_{540}\! \left(x \right) &= F_{124}\! \left(x \right) F_{356}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{541}\! \left(x \right) &= F_{542}\! \left(x \right)+F_{543}\! \left(x \right)\\ F_{542}\! \left(x \right) &= F_{356}\! \left(x \right) F_{535}\! \left(x \right)\\ F_{543}\! \left(x \right) &= F_{544}\! \left(x \right)\\ F_{544}\! \left(x \right) &= F_{28}\! \left(x \right) F_{397}\! \left(x \right) F_{49}\! \left(x \right) F_{545}\! \left(x \right)\\ F_{545}\! \left(x \right) &= -F_{535}\! \left(x \right)+F_{546}\! \left(x \right)\\ F_{546}\! \left(x \right) &= -F_{549}\! \left(x \right)+F_{547}\! \left(x \right)\\ F_{547}\! \left(x \right) &= \frac{F_{548}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}\\ F_{548}\! \left(x \right) &= F_{338}\! \left(x \right)\\ F_{549}\! \left(x \right) &= F_{330}\! \left(x \right)+F_{550}\! \left(x \right)\\ F_{550}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{4}\! \left(x \right)\\ \end{align*}

### This specification was found using the strategy pack "Insertion Point Placements Tracked Fusion Req Corrob" and has 275 rules.

Found on January 20, 2022.

Finding the specification took 14392 seconds.

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Copy 275 equations to clipboard:
\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{14}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{20}\! \left(x \right) &= 0\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{37}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x , 1\right)\\ F_{43}\! \left(x , y\right) &= F_{37}\! \left(x \right)+F_{42}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{263}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{45}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{257}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\ F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= y x\\ F_{55}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\ F_{57}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{58}\! \left(x , y\right)\\ F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\ F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)\\ F_{60}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{61}\! \left(x , y\right)\\ F_{61}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{62}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{94}\! \left(x , y\right)\\ F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\ F_{65}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{67}\! \left(x , y\right) &= F_{55}\! \left(x , y\right) F_{68}\! \left(x , y\right)\\ F_{68}\! \left(x , y\right) &= F_{69}\! \left(x , y\right)\\ F_{69}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{70}\! \left(x , y\right)\\ F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{72}\! \left(x , y\right) &= F_{18}\! \left(x \right)+F_{73}\! \left(x , y\right)\\ F_{74}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)\\ F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\ F_{77}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{78}\! \left(x , y\right)\\ F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\ F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\ F_{85}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{86}\! \left(x , y\right)\\ F_{86}\! \left(x , y\right) &= F_{20}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\ F_{87}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{85}\! \left(x , y\right)\\ F_{88}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{89}\! \left(x , y\right)\\ F_{89}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{86}\! \left(x , y\right)\\ F_{90}\! \left(x , y\right) &= F_{81}\! \left(x , y\right) F_{91}\! \left(x , y\right)\\ F_{91}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\ F_{92}\! \left(x , y\right) &= F_{18}\! \left(x \right) F_{81}\! \left(x , y\right)\\ F_{93}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{94}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\ F_{95}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{4}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{12}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{12}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{105}\! \left(x , y\right) &= -\frac{F_{76}\! \left(x , 1\right) y -F_{76}\! \left(x , y\right)}{-1+y}\\ F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)\\ F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{130}\! \left(x , y\right)\\ F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{115}\! \left(x , y\right)\\ F_{111}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{112}\! \left(x , y\right)\\ F_{112}\! \left(x , y\right) &= -\frac{y \left(F_{113}\! \left(x , 1\right)-F_{113}\! \left(x , y\right)\right)}{-1+y}\\ F_{113}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\ F_{114}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\ F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{129}\! \left(x , y\right)\\ F_{117}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{119}\! \left(x , y\right)\\ F_{118}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{47}\! \left(x , y\right)\\ F_{119}\! \left(x , y\right) &= F_{120}\! \left(x \right)+F_{124}\! \left(x , y\right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)\\ F_{125}\! \left(x , y\right) &= F_{126}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{126}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)+F_{127}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)+F_{128}\! \left(x , y\right)\\ F_{128}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{129}\! \left(x , y\right) &= -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}\\ F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)+F_{225}\! \left(x , y\right)\\ F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{153}\! \left(x , y\right)\\ F_{132}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)\\ F_{133}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{47}\! \left(x , y\right)\\ F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right)\\ F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{143}\! \left(x , y\right)\\ F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{142}\! \left(x , y\right)\\ F_{138}\! \left(x , y\right) &= -\frac{F_{139}\! \left(x , 1\right) y -F_{139}\! \left(x , y\right)}{-1+y}\\ F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)\\ F_{140}\! \left(x , y\right) &= F_{141}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{141}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{142}\! \left(x , y\right) &= -\frac{y \left(F_{124}\! \left(x , 1\right)-F_{124}\! \left(x , y\right)\right)}{-1+y}\\ F_{143}\! \left(x , y\right) &= F_{144}\! \left(x , y\right)+F_{146}\! \left(x , y\right)\\ F_{144}\! \left(x , y\right) &= -\frac{F_{145}\! \left(x , 1\right) y -F_{145}\! \left(x , y\right)}{-1+y}\\ F_{145}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{139}\! \left(x , y\right)\\ F_{146}\! \left(x , y\right) &= -\frac{y \left(F_{147}\! \left(x , 1\right)-F_{147}\! \left(x , y\right)\right)}{-1+y}\\ F_{147}\! \left(x , y\right) &= F_{148}\! \left(x , y\right)\\ F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)+F_{215}\! \left(x , y\right)\\ F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)+F_{213}\! \left(x , y\right)\\ F_{151}\! \left(x , y\right) &= F_{152}\! \left(x , y\right)+F_{153}\! \left(x , y\right)\\ F_{152}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{147}\! \left(x , y\right)\\ F_{153}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)+F_{156}\! \left(x , y\right)\\ F_{154}\! \left(x , y\right) &= F_{155}\! \left(x , y\right)\\ F_{155}\! \left(x , y\right) &= F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{156}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)+F_{158}\! \left(x , y\right)\\ F_{157}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{42}\! \left(x , y\right)\\ F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right)\\ F_{159}\! \left(x , y\right) &= F_{160}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{160}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)+F_{209}\! \left(x , y\right)\\ F_{161}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)+F_{208}\! \left(x , y\right)\\ F_{162}\! \left(x , y\right) &= -\frac{F_{163}\! \left(x , 1\right) y -F_{163}\! \left(x , y\right)}{-1+y}\\ F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)\\ F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{167}\! \left(x , y\right)\\ F_{166}\! \left(x , y\right) &= F_{37}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{168}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)+F_{172}\! \left(x \right)\\ F_{169}\! \left(x , y\right) &= F_{168}\! \left(x , y\right)+F_{171}\! \left(x , y\right)\\ F_{170}\! \left(x , y\right) &= F_{169}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{170}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\ F_{171}\! \left(x , y\right) &= F_{37}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{173}\! \left(x \right) &= -F_{179}\! \left(x \right)+F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= -F_{177}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{175}\! \left(x \right) &= \frac{F_{176}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{176}\! \left(x \right) &= F_{37}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{123}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)\\ F_{180}\! \left(x \right) &= F_{12} \left(x \right)^{2}\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{189}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{188}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x , 1\right)\\ F_{190}\! \left(x , y\right) &= -\frac{F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)}{-1+y}\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{194}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\ F_{193}\! \left(x \right) &= F_{12} \left(x \right)^{3}\\ F_{194}\! \left(x \right) &= F_{195}\! \left(x , 1\right)\\ F_{195}\! \left(x , y\right) &= -\frac{F_{196}\! \left(x , 1\right)-F_{196}\! \left(x , y\right)}{-1+y}\\ F_{196}\! \left(x , y\right) &= F_{197}\! \left(x , y\right)\\ F_{197}\! \left(x , y\right) &= F_{198}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{198}\! \left(x , y\right) &= F_{199}\! \left(x , y\right)+F_{204}\! \left(x , y\right)\\ F_{199}\! \left(x , y\right) &= F_{200}\! \left(x , y\right)+F_{203}\! \left(x , y\right)\\ F_{200}\! \left(x , y\right) &= F_{201}\! \left(x , y\right)\\ F_{201}\! \left(x , y\right) &= F_{202}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{202}\! \left(x , y\right) &= F_{200}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\ F_{203}\! \left(x , y\right) &= -\frac{y \left(F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)\right)}{-1+y}\\ F_{204}\! \left(x , y\right) &= F_{205}\! \left(x , y\right)+F_{207}\! \left(x , y\right)\\ F_{205}\! \left(x , y\right) &= F_{206}\! \left(x , y\right)\\ F_{206}\! \left(x , y\right) &= F_{12} \left(x \right)^{2} F_{52}\! \left(x , y\right)\\ F_{207}\! \left(x , y\right) &= -\frac{y \left(F_{196}\! \left(x , 1\right)-F_{196}\! \left(x , y\right)\right)}{-1+y}\\ F_{208}\! \left(x , y\right) &= -\frac{y \left(F_{162}\! \left(x , 1\right)-F_{162}\! \left(x , y\right)\right)}{-1+y}\\ F_{209}\! \left(x , y\right) &= F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)\\ F_{210}\! \left(x , y\right) &= -\frac{F_{211}\! \left(x , 1\right) y -F_{211}\! \left(x , y\right)}{-1+y}\\ F_{211}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{163}\! \left(x , y\right)\\ F_{212}\! \left(x , y\right) &= -\frac{y \left(F_{158}\! \left(x , 1\right)-F_{158}\! \left(x , y\right)\right)}{-1+y}\\ F_{213}\! \left(x , y\right) &= F_{214}\! \left(x , y\right)\\ F_{214}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{215}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{216}\! \left(x , y\right)\\ F_{216}\! \left(x , y\right) &= F_{217}\! \left(x , y\right)+F_{218}\! \left(x , y\right)\\ F_{217}\! \left(x , y\right) &= -\frac{y \left(F_{141}\! \left(x , 1\right)-F_{141}\! \left(x , y\right)\right)}{-1+y}\\ F_{218}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)+F_{219}\! \left(x , y\right)\\ F_{220}\! \left(x , y\right) &= F_{219}\! \left(x , y\right)+F_{223}\! \left(x , y\right)\\ F_{221}\! \left(x , y\right) &= F_{199}\! \left(x , y\right)+F_{220}\! \left(x , y\right)\\ F_{222}\! \left(x , y\right) &= F_{221}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{222}\! \left(x , y\right) &= F_{196}\! \left(x , y\right)\\ F_{223}\! \left(x , y\right) &= F_{224}\! \left(x , y\right)\\ F_{224}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{225}\! \left(x , y\right) &= F_{226}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\ F_{226}\! \left(x , y\right) &= F_{227}\! \left(x , y\right)+F_{251}\! \left(x , y\right)\\ F_{227}\! \left(x , y\right) &= F_{228}\! \left(x , y\right)+F_{229}\! \left(x , y\right)\\ F_{228}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{12}\! \left(x \right)\\ F_{229}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)+F_{230}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{236}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{238}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{18}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{240}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{12}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{245}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{244}\! \left(x , 1\right)\\ F_{244}\! \left(x , y\right) &= -\frac{-y F_{42}\! \left(x , y\right)+F_{42}\! \left(x , 1\right)}{-1+y}\\ F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{247}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{12}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{248}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{158}\! \left(x , 1\right)\\ F_{249}\! \left(x \right) &= F_{12}\! \left(x \right) F_{250}\! \left(x \right)\\ F_{250}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{233}\! \left(x \right)\\ F_{251}\! \left(x , y\right) &= F_{252}\! \left(x , y\right)+F_{254}\! \left(x , y\right)\\ F_{252}\! \left(x , y\right) &= F_{253}\! \left(x , y\right)\\ F_{253}\! \left(x , y\right) &= F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{254}\! \left(x , y\right) &= F_{255}\! \left(x , y\right)+F_{256}\! \left(x , y\right)\\ F_{255}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{43}\! \left(x , y\right)\\ F_{256}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)+F_{240}\! \left(x \right)\\ F_{257}\! \left(x , y\right) &= F_{258}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\ F_{258}\! \left(x , y\right) &= F_{259}\! \left(x , y\right)+F_{261}\! \left(x , y\right)\\ F_{259}\! \left(x , y\right) &= F_{260}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{260}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)+F_{66}\! \left(x \right)\\ F_{261}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{262}\! \left(x , y\right)\\ F_{262}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{263}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{264}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{268}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{264}\! \left(x \right)+F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{12}\! \left(x \right) F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{271}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{274}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{124}\! \left(x , 1\right)\\ \end{align*}

### This specification was found using the strategy pack "Point And Row Placements Tracked Fusion" and has 168 rules.

Found on October 22, 2021.

Finding the specification took 118800 seconds.

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Copy 168 equations to clipboard:
\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{27}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{27}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{27}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{7}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x , 1\right)\\ F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)\\ F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\ F_{13}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)\\ F_{14}\! \left(x , y_{0}\right) &= y_{0} x\\ F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{27}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{20}\! \left(x \right) &= 0\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x , 1\right)\\ F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{23}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right)+F_{9}\! \left(x \right)\\ F_{24}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)\\ F_{25}\! \left(x , y_{0}\right) &= F_{20}\! \left(x \right)+F_{26}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)\\ F_{26}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\ F_{28}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)\\ F_{29}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right)+F_{25}\! \left(x , y_{0}\right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x , 1\right)\\ F_{31}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)\\ F_{32}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{27}\! \left(x \right) F_{32}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{27}\! \left(x \right) F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{27}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{41}\! \left(x , 1\right)\\ F_{41}\! \left(x , y_{0}\right) &= F_{42}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)\\ F_{42}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{43}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)\\ F_{43}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{44}\! \left(x , y_{0}\right)\\ F_{44}\! \left(x , y_{0}\right) &= F_{42}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)\\ F_{45}\! \left(x , y_{0}\right) &= F_{20}\! \left(x \right)+F_{46}\! \left(x , y_{0}\right)+F_{64}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)\\ F_{46}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{47}\! \left(x , y_{0}\right)\\ F_{47}\! \left(x , y_{0}\right) &= F_{48}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)\\ F_{48}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)\\ F_{49}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right)+F_{50}\! \left(x , y_{0}\right)\\ F_{50}\! \left(x , y_{0}\right) &= F_{51}\! \left(x , y_{0}\right)\\ F_{51}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{52}\! \left(x , y_{0}\right)\\ F_{52}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right)+F_{50}\! \left(x , y_{0}\right)\\ F_{53}\! \left(x , y_{0}\right) &= F_{29}\! \left(x , y_{0}\right)+F_{54}\! \left(x , y_{0}\right)\\ F_{54}\! \left(x , y_{0}\right) &= F_{55}\! \left(x \right)+F_{59}\! \left(x , y_{0}\right)\\ F_{55}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{27}\! \left(x \right) F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{19}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{59}\! \left(x , y_{0}\right) &= 2 F_{20}\! \left(x \right)+F_{60}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)\\ F_{60}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{61}\! \left(x , y_{0}\right)\\ F_{61}\! \left(x , y_{0}\right) &= F_{50}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)\\ F_{62}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)\\ F_{63}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)\\ F_{64}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{65}\! \left(x , y_{0}\right)\\ F_{65}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{66}\! \left(x , y_{0}\right)+F_{66}\! \left(x , 1\right)}{-1+y_{0}}\\ F_{66}\! \left(x , y_{0}\right) &= 2 F_{20}\! \left(x \right)+F_{67}\! \left(x , y_{0}\right)+F_{79}\! \left(x , y_{0}\right)\\ F_{67}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{68}\! \left(x , y_{0}\right)\\ F_{68}\! \left(x , y_{0}\right) &= F_{69}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)\\ F_{69}\! \left(x , y_{0}\right) &= F_{70}\! \left(x , y_{0}\right)\\ F_{70}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)\\ F_{71}\! \left(x , y_{0}\right) &= F_{49}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}\right)\\ F_{72}\! \left(x , y_{0}\right) &= F_{55}\! \left(x \right)+F_{73}\! \left(x , y_{0}\right)\\ F_{73}\! \left(x , y_{0}\right) &= F_{74}\! \left(x , y_{0}\right)\\ F_{74}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{75}\! \left(x , y_{0}\right)\\ F_{75}\! \left(x , y_{0}\right) &= F_{73}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)\\ F_{76}\! \left(x , y_{0}\right) &= F_{77}\! \left(x , y_{0}\right)\\ F_{77}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}\right)\\ F_{78}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right)+F_{76}\! \left(x , y_{0}\right)\\ F_{79}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{80}\! \left(x , y_{0}\right)\\ F_{80}\! \left(x , y_{0}\right) &= F_{65}\! \left(x , y_{0}\right)\\ F_{81}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{45}\! \left(x , y_{0}\right)\\ F_{82}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right)\\ F_{83}\! \left(x , y_{0}\right) &= F_{84}\! \left(x , y_{0}\right)\\ F_{84}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{85}\! \left(x , y_{0}\right)\\ F_{85}\! \left(x , y_{0}\right) &= F_{86}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)\\ F_{86}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{87}\! \left(x , y_{0}\right)\\ F_{87}\! \left(x , y_{0}\right) &= F_{88}\! \left(x , 1, y_{0}\right)\\ F_{88}\! \left(x , y_{0}, y_{1}\right) &= F_{89}\! \left(x , y_{0}, y_{1}\right)+F_{90}\! \left(x , y_{0}, y_{1}\right)\\ F_{89}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{42}\! \left(x , y_{0}\right)-y_{1} F_{42}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}\\ F_{90}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{83}\! \left(x , y_{0}\right)-y_{1} F_{83}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}\\ F_{91}\! \left(x , y_{0}\right) &= F_{92}\! \left(x , y_{0}\right)\\ F_{92}\! \left(x , y_{0}\right) &= F_{27}\! \left(x \right) F_{93}\! \left(x , y_{0}\right)\\ F_{93}\! \left(x , y_{0}\right) &= F_{144}\! \left(x , y_{0}\right)+F_{94}\! \left(x , y_{0}\right)\\ F_{94}\! \left(x , y_{0}\right) &= F_{142}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)\\ F_{95}\! \left(x , y_{0}\right) &= F_{119}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}\right)\\ F_{96}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{97}\! \left(x , y_{0}\right)+F_{97}\! \left(x , 1\right)}{-1+y_{0}}\\ F_{97}\! \left(x , y_{0}\right) &= F_{87}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\ F_{98}\! \left(x , y_{0}\right) &= F_{99}\! \left(x , y_{0}\right)\\ F_{99}\! \left(x , y_{0}\right) &= F_{100}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{100}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , 1, y_{0}\right)\\ F_{101}\! \left(x , y_{0}, y_{1}\right) &= F_{102}\! \left(x , y_{1}\right)+F_{110}\! \left(x , y_{0}, y_{1}\right)\\ F_{102}\! \left(x , y_{0}\right) &= F_{103}\! \left(x , 1, y_{0}\right)\\ F_{103}\! \left(x , y_{0}, y_{1}\right) &= F_{104}\! \left(x , y_{0}, y_{1}\right)+F_{105}\! \left(x , y_{0}, y_{1}\right)\\ F_{104}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{87}\! \left(x , y_{0}\right)-y_{1} F_{87}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}\\ F_{105}\! \left(x , y_{0}, y_{1}\right) &= F_{106}\! \left(x , y_{0}, y_{1}\right)\\ F_{106}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}, y_{1}\right) F_{27}\! \left(x \right)\\ F_{107}\! \left(x , y_{0}, y_{1}\right) &= F_{108}\! \left(x , y_{0}, y_{1}\right)+F_{109}\! \left(x , y_{1}\right)\\ F_{108}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{103}\! \left(x , y_{0}, y_{1}\right)+F_{103}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\ F_{109}\! \left(x , y_{0}\right) &= F_{110}\! \left(x , 1, y_{0}\right)\\ F_{111}\! \left(x , y_{0}, y_{1}\right) &= F_{110}\! \left(x , y_{0} y_{1}, y_{1}\right)\\ F_{111}\! \left(x , y_{0}, y_{1}\right) &= F_{112}\! \left(x , y_{0}, y_{1}\right)+F_{118}\! \left(x , y_{0}, y_{1}\right)+F_{20}\! \left(x \right)\\ F_{112}\! \left(x , y_{0}, y_{1}\right) &= F_{113}\! \left(x , y_{0}, y_{1}\right) F_{27}\! \left(x \right)\\ F_{113}\! \left(x , y_{0}, y_{1}\right) &= F_{111}\! \left(x , y_{0}, y_{1}\right)+F_{114}\! \left(x , y_{0}, y_{1}\right)\\ F_{114}\! \left(x , y_{0}, y_{1}\right) &= F_{115}\! \left(x , y_{1}\right) F_{41}\! \left(x , y_{1}\right)\\ F_{115}\! \left(x , y_{0}\right) &= F_{116}\! \left(x , y_{0}\right)\\ F_{116}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{117}\! \left(x \right) F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\ F_{117}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{118}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{1}\right) F_{87}\! \left(x , y_{1}\right)\\ F_{119}\! \left(x , y_{0}\right) &= F_{120}\! \left(x , y_{0}\right)\\ F_{120}\! \left(x , y_{0}\right) &= F_{121}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{121}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{122}\! \left(x , y_{0}\right)+F_{122}\! \left(x , 1\right)}{-1+y_{0}}\\ F_{122}\! \left(x , y_{0}\right) &= F_{123}\! \left(x , y_{0}\right)+F_{134}\! \left(x , y_{0}\right)\\ F_{123}\! \left(x , y_{0}\right) &= F_{124}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)\\ F_{124}\! \left(x , y_{0}\right) &= F_{125}\! \left(x , y_{0}\right)+F_{87}\! \left(x , y_{0}\right)\\ F_{125}\! \left(x , y_{0}\right) &= F_{126}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{126}\! \left(x , y_{0}\right) &= F_{127}\! \left(x , y_{0}\right)+F_{130}\! \left(x , y_{0}\right)\\ F_{127}\! \left(x , y_{0}\right) &= F_{128}\! \left(x , 1, y_{0}\right)\\ F_{128}\! \left(x , y_{0}, y_{1}\right) &= F_{129}\! \left(x , y_{0}, 1, y_{1}\right)\\ F_{129}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{88}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{88}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}\\ F_{130}\! \left(x , y_{0}\right) &= F_{131}\! \left(x , 1, y_{0}\right)\\ F_{131}\! \left(x , y_{0}, y_{1}\right) &= F_{132}\! \left(x , y_{0}, y_{1}\right) F_{27}\! \left(x \right)\\ F_{132}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{133}\! \left(x , y_{0}, y_{1}\right)+F_{133}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\ F_{133}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{131}\! \left(x , y_{0}, y_{1}\right)\\ F_{134}\! \left(x , y_{0}\right) &= F_{135}\! \left(x , y_{0}\right)+F_{140}\! \left(x , y_{0}\right)+F_{20}\! \left(x \right)\\ F_{135}\! \left(x , y_{0}\right) &= F_{136}\! \left(x , y_{0}\right)\\ F_{136}\! \left(x , y_{0}\right) &= F_{137}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{137}\! \left(x , y_{0}\right) &= F_{122}\! \left(x , y_{0}\right)+F_{138}\! \left(x , y_{0}\right)\\ F_{138}\! \left(x , y_{0}\right) &= F_{139}\! \left(x , y_{0}\right)\\ F_{139}\! \left(x , y_{0}\right) &= F_{117}\! \left(x \right) F_{124}\! \left(x , y_{0}\right) F_{27}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{140}\! \left(x , y_{0}\right) &= F_{141}\! \left(x , y_{0}\right)\\ F_{141}\! \left(x , y_{0}\right) &= F_{19}\! \left(x \right) F_{27}\! \left(x \right) F_{87}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)\\ F_{142}\! \left(x , y_{0}\right) &= F_{143}\! \left(x , y_{0}\right)\\ F_{143}\! \left(x , y_{0}\right) &= F_{100}\! \left(x , y_{0}\right) F_{11}\! \left(x , y_{0}\right)\\ F_{144}\! \left(x , y_{0}\right) &= F_{145}\! \left(x , y_{0}\right)+F_{158}\! \left(x , y_{0}\right)\\ F_{145}\! \left(x , y_{0}\right) &= F_{146}\! \left(x , y_{0}\right)+F_{150}\! \left(x , y_{0}\right)+F_{157}\! \left(x , y_{0}\right)+F_{20}\! \left(x \right)\\ F_{146}\! \left(x , y_{0}\right) &= F_{147}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{147}\! \left(x , y_{0}\right) &= F_{145}\! \left(x , y_{0}\right)+F_{148}\! \left(x , y_{0}\right)\\ F_{148}\! \left(x , y_{0}\right) &= F_{149}\! \left(x , y_{0}\right)\\ F_{149}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{117}\! \left(x \right) F_{124}\! \left(x , y_{0}\right) F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\ F_{150}\! \left(x , y_{0}\right) &= F_{151}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)\\ F_{151}\! \left(x , y_{0}\right) &= F_{152}\! \left(x , y_{0}\right)\\ F_{152}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{153}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)\\ F_{153}\! \left(x , y_{0}\right) &= F_{154}\! \left(x , y_{0}\right)+F_{156}\! \left(x , y_{0}\right)\\ F_{154}\! \left(x , y_{0}\right) &= F_{155}\! \left(x , y_{0}\right)\\ F_{155}\! \left(x , y_{0}\right) &= F_{126}\! \left(x , y_{0}\right) F_{13}\! \left(x , y_{0}\right)\\ F_{156}\! \left(x , y_{0}\right) &= F_{53}\! \left(x , y_{0}\right) F_{87}\! \left(x , y_{0}\right)\\ F_{157}\! \left(x , y_{0}\right) &= F_{118}\! \left(x , 1, y_{0}\right)\\ F_{158}\! \left(x , y_{0}\right) &= F_{159}\! \left(x , y_{0}\right)\\ F_{159}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right) F_{160}\! \left(x , y_{0}\right)\\ F_{160}\! \left(x , y_{0}\right) &= \frac{y_{0} \left(F_{111}\! \left(x , 1, y_{0}\right)-F_{111}\! \left(x , \frac{1}{y_{0}}, y_{0}\right)\right)}{-1+y_{0}}\\ F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{163}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{165}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{97}\! \left(x , 1\right)\\ F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{167}\! \left(x \right) &= F_{122}\! \left(x , 1\right)\\ \end{align*}

### This specification was found using the strategy pack "Point And Row And Col Placements Tracked Fusion Req Corrob" and has 124 rules.

Found on June 04, 2021.

Finding the specification took 35083 seconds.

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Copy 124 equations to clipboard:
\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x , 1\right)\\ F_{13}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{16}\! \left(x , y\right)\\ F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{15}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{20}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{5}\! \left(x \right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{26}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{27}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\ F_{27}\! \left(x \right) &= 0\\ F_{28}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{29}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= y x\\ F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\ F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{33}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{80}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{37}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{38}\! \left(x , y\right)\\ F_{38}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)\\ F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\ F_{40}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{38}\! \left(x , y\right)\\ F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\ F_{42}\! \left(x , y\right) &= F_{38}\! \left(x , y\right) F_{4}\! \left(x \right) F_{43}\! \left(x , y\right)\\ F_{43}\! \left(x , y\right) &= -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}\\ F_{44}\! \left(x , y\right) &= F_{45}\! \left(x \right)+F_{54}\! \left(x , y\right)\\ F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{53}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{55}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)\\ F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)\\ F_{57}\! \left(x , y\right) &= F_{27}\! \left(x \right)+F_{56}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\ F_{57}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)+F_{58}\! \left(x , y\right)\\ F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)\\ F_{59}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{60}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\ F_{61}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)\\ F_{62}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{38}\! \left(x , y\right) F_{63}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\ F_{64}\! \left(x , y\right) &= F_{65}\! \left(x \right)+F_{71}\! \left(x , y\right)\\ F_{65}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{4}\! \left(x \right) F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{12}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{4}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{71}\! \left(x , y\right) &= F_{72}\! \left(x , y\right)\\ F_{72}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{73}\! \left(x , y\right)\\ F_{73}\! \left(x , y\right) &= F_{65}\! \left(x \right)+F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\ F_{74}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{75}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}\\ F_{76}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{73}\! \left(x , y\right)\\ F_{77}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{73}\! \left(x , y\right)\\ F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)\\ F_{79}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{80}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{81}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}\\ F_{83}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{84}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}\\ F_{85}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right) F_{91}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{4}\! \left(x \right) F_{88}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{94}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{57}\! \left(x , 1\right)\\ F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{4}\! \left(x \right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{98}\! \left(x , 1\right)\\ F_{98}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{99}\! \left(x , y\right)\\ F_{99}\! \left(x , y\right) &= -\frac{y \left(F_{57}\! \left(x , 1\right)-F_{57}\! \left(x , y\right)\right)}{-1+y}\\ F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{101}\! \left(x , y\right) &= -\frac{y \left(F_{98}\! \left(x , 1\right)-F_{98}\! \left(x , y\right)\right)}{-1+y}\\ F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\ F_{103}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)\\ F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)+F_{110}\! \left(x , y\right)\\ F_{108}\! \left(x , y\right) &= F_{107}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{98}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\ F_{109}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{98}\! \left(x , y\right)\\ F_{111}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{114}\! \left(x , y\right)\\ F_{112}\! \left(x , y\right) &= F_{111}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\ F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\ F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{117}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{118}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{118}\! \left(x , y\right) &= -\frac{y \left(F_{23}\! \left(x , 1\right)-F_{23}\! \left(x , y\right)\right)}{-1+y}\\ F_{119}\! \left(x , y\right) &= F_{114}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{120}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{85}\! \left(x , 1\right)\\ \end{align*}

### This specification was found using the strategy pack "Insertion Point Placements Tracked Fusion" and has 274 rules.

Found on January 20, 2022.

Finding the specification took 13730 seconds.

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\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{4}\! \left(x \right) &= x\\ F_{5}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{14}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{15}\! \left(x \right) &= F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{24}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{20}\! \left(x \right) &= 0\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{263}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{36}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{11}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{37}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{40}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x , 1\right)\\ F_{43}\! \left(x , y\right) &= F_{37}\! \left(x \right)+F_{42}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{262}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\ F_{45}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{45}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\ F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\ F_{48}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)\\ F_{49}\! \left(x , y\right) &= F_{256}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\ F_{50}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\ F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\ F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\ F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{54}\! \left(x , y\right) &= y x\\ F_{55}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)\\ F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\ F_{57}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{58}\! \left(x , y\right)\\ F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\ F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)\\ F_{60}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{61}\! \left(x , y\right)\\ F_{61}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\ F_{62}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{94}\! \left(x , y\right)\\ F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\ F_{65}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{67}\! \left(x , y\right) &= F_{55}\! \left(x , y\right) F_{68}\! \left(x , y\right)\\ F_{68}\! \left(x , y\right) &= F_{69}\! \left(x , y\right)\\ F_{69}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{70}\! \left(x , y\right)\\ F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\ F_{71}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{72}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{73}\! \left(x , y\right)\\ F_{74}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\ F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)\\ F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\ F_{77}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{78}\! \left(x , y\right)\\ F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\ F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\ F_{80}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\ F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\ F_{84}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\ F_{85}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{86}\! \left(x , y\right)\\ F_{86}\! \left(x , y\right) &= F_{20}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\ F_{87}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{85}\! \left(x , y\right)\\ F_{88}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{89}\! \left(x , y\right)\\ F_{89}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{86}\! \left(x , y\right)\\ F_{90}\! \left(x , y\right) &= F_{81}\! \left(x , y\right) F_{91}\! \left(x , y\right)\\ F_{91}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\ F_{92}\! \left(x , y\right) &= F_{24}\! \left(x \right) F_{81}\! \left(x , y\right)\\ F_{93}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{94}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\ F_{95}\! \left(x , y\right) &= F_{52}\! \left(x , y\right) F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{4}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{12}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\ F_{104}\! \left(x , y\right) &= -\frac{F_{76}\! \left(x , 1\right) y -F_{76}\! \left(x , y\right)}{-1+y}\\ F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)\\ F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)+F_{129}\! \left(x , y\right)\\ F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{114}\! \left(x , y\right)\\ F_{110}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{111}\! \left(x , y\right)\\ F_{111}\! \left(x , y\right) &= -\frac{y \left(F_{112}\! \left(x , 1\right)-F_{112}\! \left(x , y\right)\right)}{-1+y}\\ F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\ F_{113}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\ F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right)+F_{128}\! \left(x , y\right)\\ F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{118}\! \left(x , y\right)\\ F_{117}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{47}\! \left(x , y\right)\\ F_{118}\! \left(x , y\right) &= F_{119}\! \left(x \right)+F_{123}\! \left(x , y\right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)\\ F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{125}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{126}\! \left(x , y\right)\\ F_{126}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{127}\! \left(x , y\right)\\ F_{127}\! \left(x , y\right) &= F_{123}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{128}\! \left(x , y\right) &= -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}\\ F_{129}\! \left(x , y\right) &= F_{130}\! \left(x , y\right)+F_{224}\! \left(x , y\right)\\ F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)+F_{152}\! \left(x , y\right)\\ F_{131}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)\\ F_{132}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{47}\! \left(x , y\right)\\ F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)\\ F_{134}\! \left(x , y\right) &= F_{135}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right)+F_{142}\! \left(x , y\right)\\ F_{136}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{141}\! \left(x , y\right)\\ F_{137}\! \left(x , y\right) &= -\frac{F_{138}\! \left(x , 1\right) y -F_{138}\! \left(x , y\right)}{-1+y}\\ F_{138}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)\\ F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{140}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\ F_{141}\! \left(x , y\right) &= -\frac{y \left(F_{123}\! \left(x , 1\right)-F_{123}\! \left(x , y\right)\right)}{-1+y}\\ F_{142}\! \left(x , y\right) &= F_{143}\! \left(x , y\right)+F_{145}\! \left(x , y\right)\\ F_{143}\! \left(x , y\right) &= -\frac{F_{144}\! \left(x , 1\right) y -F_{144}\! \left(x , y\right)}{-1+y}\\ F_{144}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{138}\! \left(x , y\right)\\ F_{145}\! \left(x , y\right) &= -\frac{y \left(F_{146}\! \left(x , 1\right)-F_{146}\! \left(x , y\right)\right)}{-1+y}\\ F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y\right)\\ F_{147}\! \left(x , y\right) &= F_{148}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)+F_{214}\! \left(x , y\right)\\ F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)+F_{212}\! \left(x , y\right)\\ F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)+F_{152}\! \left(x , y\right)\\ F_{151}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{146}\! \left(x , y\right)\\ F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , y\right)+F_{155}\! \left(x , y\right)\\ F_{153}\! \left(x , y\right) &= F_{154}\! \left(x , y\right)\\ F_{154}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{24}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)+F_{157}\! \left(x , y\right)\\ F_{156}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{42}\! \left(x , y\right)\\ F_{157}\! \left(x , y\right) &= F_{158}\! \left(x , y\right)\\ F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{159}\! \left(x , y\right) &= F_{160}\! \left(x , y\right)+F_{208}\! \left(x , y\right)\\ F_{160}\! \left(x , y\right) &= F_{161}\! \left(x , y\right)+F_{207}\! \left(x , y\right)\\ F_{161}\! \left(x , y\right) &= -\frac{F_{162}\! \left(x , 1\right) y -F_{162}\! \left(x , y\right)}{-1+y}\\ F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right)\\ F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)\\ F_{165}\! \left(x , y\right) &= F_{37}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{167}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{171}\! \left(x \right)\\ F_{168}\! \left(x , y\right) &= F_{167}\! \left(x , y\right)+F_{170}\! \left(x , y\right)\\ F_{169}\! \left(x , y\right) &= F_{168}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\ F_{169}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\ F_{170}\! \left(x , y\right) &= F_{37}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{172}\! \left(x \right) &= -F_{178}\! \left(x \right)+F_{173}\! \left(x \right)\\ F_{173}\! \left(x \right) &= -F_{176}\! \left(x \right)+F_{174}\! \left(x \right)\\ F_{174}\! \left(x \right) &= \frac{F_{175}\! \left(x \right)}{F_{4}\! \left(x \right)}\\ F_{175}\! \left(x \right) &= F_{37}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{122}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{179}\! \left(x \right)+F_{180}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{12} \left(x \right)^{2}\\ F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{190}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{187}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{185}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{189}\! \left(x , 1\right)\\ F_{189}\! \left(x , y\right) &= -\frac{F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)}{-1+y}\\ F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\ F_{192}\! \left(x \right) &= F_{12} \left(x \right)^{3}\\ F_{193}\! \left(x \right) &= F_{194}\! \left(x , 1\right)\\ F_{194}\! \left(x , y\right) &= -\frac{F_{195}\! \left(x , 1\right)-F_{195}\! \left(x , y\right)}{-1+y}\\ F_{195}\! \left(x , y\right) &= F_{196}\! \left(x , y\right)\\ F_{196}\! \left(x , y\right) &= F_{197}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{197}\! \left(x , y\right) &= F_{198}\! \left(x , y\right)+F_{203}\! \left(x , y\right)\\ F_{198}\! \left(x , y\right) &= F_{199}\! \left(x , y\right)+F_{202}\! \left(x , y\right)\\ F_{199}\! \left(x , y\right) &= F_{200}\! \left(x , y\right)\\ F_{200}\! \left(x , y\right) &= F_{201}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{201}\! \left(x , y\right) &= F_{199}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\ F_{202}\! \left(x , y\right) &= -\frac{y \left(F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)\right)}{-1+y}\\ F_{203}\! \left(x , y\right) &= F_{204}\! \left(x , y\right)+F_{206}\! \left(x , y\right)\\ F_{204}\! \left(x , y\right) &= F_{205}\! \left(x , y\right)\\ F_{205}\! \left(x , y\right) &= F_{12} \left(x \right)^{2} F_{52}\! \left(x , y\right)\\ F_{206}\! \left(x , y\right) &= -\frac{y \left(F_{195}\! \left(x , 1\right)-F_{195}\! \left(x , y\right)\right)}{-1+y}\\ F_{207}\! \left(x , y\right) &= -\frac{y \left(F_{161}\! \left(x , 1\right)-F_{161}\! \left(x , y\right)\right)}{-1+y}\\ F_{208}\! \left(x , y\right) &= F_{209}\! \left(x , y\right)+F_{211}\! \left(x , y\right)\\ F_{209}\! \left(x , y\right) &= -\frac{F_{210}\! \left(x , 1\right) y -F_{210}\! \left(x , y\right)}{-1+y}\\ F_{210}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{162}\! \left(x , y\right)\\ F_{211}\! \left(x , y\right) &= -\frac{y \left(F_{157}\! \left(x , 1\right)-F_{157}\! \left(x , y\right)\right)}{-1+y}\\ F_{212}\! \left(x , y\right) &= F_{213}\! \left(x , y\right)\\ F_{213}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{214}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{215}\! \left(x , y\right)\\ F_{215}\! \left(x , y\right) &= F_{216}\! \left(x , y\right)+F_{217}\! \left(x , y\right)\\ F_{216}\! \left(x , y\right) &= -\frac{y \left(F_{140}\! \left(x , 1\right)-F_{140}\! \left(x , y\right)\right)}{-1+y}\\ F_{217}\! \left(x , y\right) &= F_{152}\! \left(x , y\right)+F_{218}\! \left(x , y\right)\\ F_{219}\! \left(x , y\right) &= F_{218}\! \left(x , y\right)+F_{222}\! \left(x , y\right)\\ F_{220}\! \left(x , y\right) &= F_{198}\! \left(x , y\right)+F_{219}\! \left(x , y\right)\\ F_{221}\! \left(x , y\right) &= F_{220}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{221}\! \left(x , y\right) &= F_{195}\! \left(x , y\right)\\ F_{222}\! \left(x , y\right) &= F_{223}\! \left(x , y\right)\\ F_{223}\! \left(x , y\right) &= F_{25}\! \left(x \right) F_{52}\! \left(x , y\right)\\ F_{224}\! \left(x , y\right) &= F_{225}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\ F_{225}\! \left(x , y\right) &= F_{226}\! \left(x , y\right)+F_{250}\! \left(x , y\right)\\ F_{226}\! \left(x , y\right) &= F_{227}\! \left(x , y\right)+F_{228}\! \left(x , y\right)\\ F_{227}\! \left(x , y\right) &= F_{117}\! \left(x , y\right) F_{12}\! \left(x \right)\\ F_{228}\! \left(x , y\right) &= F_{146}\! \left(x , y\right)+F_{229}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{231}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{248}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{235}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{234}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{237}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{2}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{239}\! \left(x \right)\\ F_{238}\! \left(x \right) &= F_{12}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{241}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{244}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x , 1\right)\\ F_{243}\! \left(x , y\right) &= -\frac{-y F_{42}\! \left(x , y\right)+F_{42}\! \left(x , 1\right)}{-1+y}\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)+F_{246}\! \left(x \right)\\ F_{245}\! \left(x \right) &= F_{12}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{157}\! \left(x , 1\right)\\ F_{248}\! \left(x \right) &= F_{12}\! \left(x \right) F_{249}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{232}\! \left(x \right)\\ F_{250}\! \left(x , y\right) &= F_{251}\! \left(x , y\right)+F_{253}\! \left(x , y\right)\\ F_{251}\! \left(x , y\right) &= F_{252}\! \left(x , y\right)\\ F_{252}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{24}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{253}\! \left(x , y\right) &= F_{254}\! \left(x , y\right)+F_{255}\! \left(x , y\right)\\ F_{254}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{43}\! \left(x , y\right)\\ F_{255}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)+F_{239}\! \left(x \right)\\ F_{256}\! \left(x , y\right) &= F_{257}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\ F_{257}\! \left(x , y\right) &= F_{258}\! \left(x , y\right)+F_{260}\! \left(x , y\right)\\ F_{258}\! \left(x , y\right) &= F_{259}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\ F_{259}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)+F_{66}\! \left(x \right)\\ F_{260}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{261}\! \left(x , y\right)\\ F_{261}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{30}\! \left(x \right)\\ F_{262}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{55}\! \left(x , y\right)\\ F_{263}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{267}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{263}\! \left(x \right)+F_{268}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{12}\! \left(x \right) F_{269}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{272}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{273}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{123}\! \left(x , 1\right)\\ \end{align*}