Av(13452, 13524, 13542, 14352, 14523, 14532, 15234, 15243, 15324, 15342, 15423, 15432, 41352, 41523, 41532)
View Raw Data
Counting Sequence
1, 1, 2, 6, 24, 105, 479, 2248, 10809, 53047, 264742, 1339494, 6854857, 35418270, 184515160, ...
Implicit Equation for the Generating Function
\(\displaystyle 2 x^{5} F \left(x \right)^{8}-2 \left(3 x -1\right) x^{4} F \left(x \right)^{7}+2 x^{4} \left(3 x -4\right) F \left(x \right)^{6}-x^{2} \left(2 x^{3}-9 x^{2}+3 x -1\right) F \left(x \right)^{5}-x^{2} \left(3 x^{2}-3 x +2\right) F \left(x \right)^{4}+2 x \left(x -1\right) F \left(x \right)^{3}-x \left(x -3\right) F \left(x \right)^{2}+\left(-2 x +1\right) F \! \left(x \right)-1 = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 24\)
\(\displaystyle a \! \left(5\right) = 105\)
\(\displaystyle a \! \left(6\right) = 479\)
\(\displaystyle a \! \left(7\right) = 2248\)
\(\displaystyle a \! \left(8\right) = 10809\)
\(\displaystyle a \! \left(9\right) = 53047\)
\(\displaystyle a \! \left(10\right) = 264742\)
\(\displaystyle a \! \left(11\right) = 1339494\)
\(\displaystyle a \! \left(12\right) = 6854857\)
\(\displaystyle a \! \left(13\right) = 35418270\)
\(\displaystyle a \! \left(14\right) = 184515160\)
\(\displaystyle a \! \left(15\right) = 968139155\)
\(\displaystyle a \! \left(16\right) = 5111616701\)
\(\displaystyle a \! \left(17\right) = 27137811917\)
\(\displaystyle a \! \left(18\right) = 144784317602\)
\(\displaystyle a \! \left(19\right) = 775843858301\)
\(\displaystyle a \! \left(20\right) = 4173906840460\)
\(\displaystyle a \! \left(21\right) = 22535307734715\)
\(\displaystyle a \! \left(22\right) = 122066218156248\)
\(\displaystyle a \! \left(23\right) = 663156545684486\)
\(\displaystyle a \! \left(24\right) = 3612583119190472\)
\(\displaystyle a \! \left(25\right) = 19729058831475151\)
\(\displaystyle a \! \left(26\right) = 107993603082726359\)
\(\displaystyle a \! \left(27\right) = 592404751203001855\)
\(\displaystyle a \! \left(28\right) = 3256128432478689326\)
\(\displaystyle a \! \left(29\right) = 17930298780759975619\)
\(\displaystyle a \! \left(30\right) = 98906081105282264602\)
\(\displaystyle a \! \left(31\right) = 546461503041067809851\)
\(\displaystyle a \! \left(32\right) = 3023802592126616259360\)
\(\displaystyle a \! \left(33\right) = 16755783530318188828163\)
\(\displaystyle a \! \left(34\right) = 92973068385626943339462\)
\(\displaystyle a \! \left(35\right) = 516532309114758530927237\)
\(\displaystyle a \! \left(36\right) = 2873130014219213703730245\)
\(\displaystyle a \! \left(37\right) = 15999357747359067620401707\)
\(\displaystyle a \! \left(38\right) = 89189460159839150639654317\)
\(\displaystyle a \! \left(39\right) = 497696344898286629634000356\)
\(\displaystyle a \! \left(40\right) = 2779926388329976430098977469\)
\(\displaystyle a \! \left(41\right) = 15541741394758091185725900746\)
\(\displaystyle a \! \left(42\right) = 86965032424743407610728398743\)
\(\displaystyle a \! \left(43\right) = 487024307345377028828455060407\)
\(\displaystyle a \! \left(44\right) = 2729613693842429849941665497369\)
\(\displaystyle a \! \left(45\right) = 15310204714403663197415211877570\)
\(\displaystyle a \! \left(46\right) = 85936121057032489175456436782173\)
\(\displaystyle a \! \left(47\right) = 482694144626952499959259571971907\)
\(\displaystyle a \! \left(48\right) = 2713046779434155499620080457918694\)
\(\displaystyle a \! \left(49\right) = 15258776221764435789530048348546904\)
\(\displaystyle a \! \left(50\right) = 85871333377125607059802830153691713\)
\(\displaystyle a \! \left(51\right) = 483539940665611557159347175092460972\)
\(\displaystyle a \! \left(52\right) = 2724346280551653354060821939994572371\)
\(\displaystyle a \! \left(53\right) = 15357792458138603716774053039301547741\)
\(\displaystyle a \! \left(54\right) = 86620971228920525127778652504312856527\)
\(\displaystyle a \! \left(55\right) = 488806291795931150058522471781112572820\)
\(\displaystyle a \! \left(56\right) = 2759701878851898813422457856034983374676\)
\(\displaystyle a \! \left(57\right) = 15588049154723242184888768583556941406416\)
\(\displaystyle a \! \left(58\right) = 88088362309977291622937041905826682619001\)
\(\displaystyle a \! \left(59\right) = 498007395039993427159861821192239183778599\)
\(\displaystyle a \! \left(60\right) = 2816677879814767857019434159166983224692022\)
\(\displaystyle a \! \left(61\right) = 15937370593288685196903596208420295723953899\)
\(\displaystyle a \! \left(62\right) = 90212872229799616076127752922602212620197723\)
\(\displaystyle a \! \left(63\right) = 510842741462490021241957661080759999966220118\)
\(\displaystyle a \! \left(64\right) = 2893793955888031027594196239828562815360013842\)
\(\displaystyle a \! \left(65\right) = 16398520606307828989589898230494023166791747933\)
\(\displaystyle a \! \left(66\right) = 92959477033004651162296727457727440996451524846\)
\(\displaystyle a \! \left(67\right) = 527144979289142381886651375769855277191275883472\)
\(\displaystyle a \! \left(68\right) = 2990264064123766086143079044416660293330944024425\)
\(\displaystyle a \! \left(69\right) = 16967893343460157857629767495190698502774755652922\)
\(\displaystyle a \! \left(70\right) = 96312189612564980217017725641018685912139979569692\)
\(\displaystyle a \! \left(71\right) = 546846871654294181379747520365141964798549643481081\)
\(\displaystyle a \! \left(72\right) = 3105830199873897681138071444643434269544069842133194\)
\(\displaystyle a \! \left(73\right) = 17644676168900168644946533861461295128777416425973799\)
\(\displaystyle a \! \left(74\right) = 100269842021910247781728626596068979942411139751810914\)
\(\displaystyle a \! \left(75\right) = 569960036872743316963765386133482194003467432620493686\)
\(\displaystyle a \! \left(76\right) = 3240655210290736868687861161396369699464911448788102555\)
\(\displaystyle a \! \left(77\right) = 18430309249977434487688300788096495793738638784093726625\)
\(\displaystyle a \! \left(78\right) = 104843361501507616169638957609013529880347834487657579769\)
\(\displaystyle a \! \left(79\right) = 596561225262632442112391914107344551182125837717778139868\)
\(\displaystyle a \! \left(80\right) = 3395253715810800234093301197115295034473410877305368014435\)
\(\displaystyle a \! \left(81\right) = 19328138252118853131464194342872744107927720450649870258213\)
\(\displaystyle a \! \left(82\right) = 110054027156610707566266594416861123173949220990293029928193\)
\(\displaystyle a \! \left(83\right) = 626783586829034636342640166826214194470476340161874916720726\)
\(\displaystyle a \! \left(84\right) = 3570448487387219269346142351894296588145105599563341789750541\)
\(\displaystyle a \! \left(85\right) = 20343197157189626530766895634381268998370320422903957371232470\)
\(\displaystyle a \! \left(86\right) = 115932393284285952916969656205239898339448227105756304900117278\)
\(\displaystyle a \! \left(87\right) = 660811362101096291922437813520842282138934007017581146368118322\)
\(\displaystyle a \! \left(88\right) = 3767344441876556530223152468983148703391207458058103031379435691\)
\(\displaystyle a \! \left(89\right) = 21482081972623654427313080809503963574198905955645502785799589733\)
\(\displaystyle a \! \left(90\right) = 122517682731991681754144316573151140047807783791800274275475585699\)
\(\displaystyle a \! \left(91\right) = 698877009694961031233916527511646055195365886548902994005643529701\)
\(\displaystyle a \! \left(92\right) = 3987315301836782580578337078453717949264219988274035840035261321329\)
\(\displaystyle a \! \left(93\right) = 22752890432316369559933376994529929775030161108410265895302521598615\)
\(\displaystyle a \! \left(94\right) = 129857525042076623915219526193367897530703494792572988631751933426760\)
\(\displaystyle a \! \left(95\right) = 741260140192256363886375654938019092109068785354221272724453261363431\)
\(\displaystyle a \! \left(96\right) = 4231999744999845682880831112810621420517932651715351253015695609377997\)
\(\displaystyle a \! \left(97\right) = 24165211695375116517537311215658258695882247004285233452479100055675363\)
\(\displaystyle a \! \left(98\right) = 138007958789418731432799809691133537324460828228766681772821725622908745\)
\(\displaystyle a \! \left(99\right) = 788287850211024385904584009607790611862335855316066399426389778845019880\)
\(\displaystyle a \! \left(100\right) = 4503304997183014271846068716367627760675912252177212224968431677394338102\)
\(\displaystyle a \! \left(101\right) = 25730155736587987442140802251944885543576875987863909608311475677693653172\)
\(\displaystyle a \! \left(102\right) = 147033646235550335743113185874747538960196689843967963746177011073295834567\)
\(\displaystyle a \! \left(103\right) = 840336195776693426753747354034414822302995716514797065434462330329271937994\)
\(\displaystyle a \! \left(104\right) = 4803416558180187862031430099137268244455880278521226699056432386678556694848\)
\(\displaystyle a \! \left(105\right) = 27460415856676498629996477322016283228277280052604374275984773742943573964162\)
\(\displaystyle a \! \left(106\right) = 157008267408275191862897462517407007791963822552183664045385038893999797046907\)
\(\displaystyle a \! \left(107\right) = 897832640804412190582074603127626446497457525494384797323991900912994740732705\)
\(\displaystyle a \! \left(108\right) = 5134813243652071566631674140841906035243552638890179158919688149598513857272162\)
\(\displaystyle a \! \left(109\right) = 29370360263403725840203305061250850815458078460216813012129923261222115621573394\)
\(\displaystyle a \! \left(110\right) = 168015073640409450963217325915018505327508591413958389051105751324353763659973146\)
\(\displaystyle a \! \left(111\right) = 961259382846557477978421698001816508221253634609174750320522732113034106111277119\)
\(\displaystyle a \! \left(112\right) = 5500287067280095805036722557985963747497110266993270291718839513702249429820146182\)
\(\displaystyle a \! \left(113\right) = 31476150433650489411447884098164898036730885799728080890326045791834999281734376921\)
\(\displaystyle a \! \left(114\right) = 180147589688897019090003138421278986059006804972805229407343831888753698919475869185\)
\(\displaystyle a \! \left(115\right) = 1031157505316348158860322529407748896441842373945832273775748068421491859762546628597\)
\(\displaystyle a \! \left(n +116\right) = -\frac{123830272 \left(n +2\right) \left(n +3\right) \left(n +4\right) \left(n +5\right) \left(759901776802523881152516328397 n^{3}+11709807699699663735639655758541 n^{2}+55846379309823735327188091882344 n +78152063431554108569395712090910\right) a \! \left(n +2\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(230423537585615017959520195 n^{6}+153196084902142677460402190409 n^{5}+42437073724689858048742015098631 n^{4}+6269457155214565917524228461179975 n^{3}+520984531610453384349192947015761078 n^{2}+23089053441786630709126598506817205120 n +426347469939118657920001143288008151600\right) a \! \left(n +112\right)}{241436472567575687500 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(2 n +233\right)}+\frac{\left(4188088588302384512735 n^{5}+3530877725134254043771843 n^{4}+1058090594698523940883999713 n^{3}+148608423261510836748357303149 n^{2}+10017715770102629043119879511616 n +262599192477340143321687056373072\right) a \! \left(n +113\right)}{6898184930502162500 \left(n +115\right) \left(2 n +233\right) \left(2 n +231\right) \left(n +117\right) \left(n +116\right)}-\frac{\left(55606805134249908083448846077426314509293911709740143391207 n^{7}+23636336198516200946744465730942504430567716743570733820889985 n^{6}+4306203074453560138161497621987639562266822805440827769863513339 n^{5}+435895828429626594246238989967656693495774221760578733232025452305 n^{4}+26477462530361300680359363232726863429276055243522788280800359523538 n^{3}+965125243450696560545263850224835539689214587141385306136910506209830 n^{2}+19547423012767972158861549214971757267426370871979058858289419828087316 n +169706549539938778249958792121129623463864884948713958537993015779273440\right) a \! \left(n +62\right)}{12071823628378784375000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(76763945574357616054525840099937860616620778798168357710081 n^{7}+32856188517229269557226173901597825363327273528649872109638465 n^{6}+6024896163713556469033076461797345919756138939189476871591960801 n^{5}+613550915486996162508317862596658096584045727642160360050941913180 n^{4}+37474429903752585014138248479067122314629697982967240718005701218944 n^{3}+1372754244602249160009573860853980658757313553499595949136394322091035 n^{2}+27924727358358479254881698421586027376858032418397384176072055809910294 n +243336198418346386478481492996918144193352271741668132351055809227683360\right) a \! \left(n +63\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(31382229092236394768122246120482081385452596023038235075438 n^{7}+15014317432699531420107222284640164346460230230394063175325069 n^{6}+3064057209747755968929230135611225461114561737134421274425045875 n^{5}+345978145477361452347216182935608016842087307539043118748125346065 n^{4}+23357198151415070362458049979335269696346153923282506362802886505807 n^{3}+943213250237950785984474121373588446390472177181274701945467050874426 n^{2}+21103687833358235114856847861722395507229102362251306355900388989539080 n +201884665521296882522390376502292703914139306263115793754351656009556160\right) a \! \left(n +64\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(36264616448054096612177511221866366756817941775270784486492 n^{7}+16632853598498513223766443761385308694726485254773471551265436 n^{6}+3269237745279486647935635326669845756089345239801089713452547303 n^{5}+356976434576360976958232871622485033642054789060910926789375486640 n^{4}+23387424956171209031466678816664119376060774257670287343072403047533 n^{3}+919364317479263499080229152918771136704158648961898179675518040116084 n^{2}+20079082818710830916417646733488532039269929012987425184663937363253512 n +187957207619454983439501230801262948285030011465307521434498311419832360\right) a \! \left(n +65\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(4204914099729021114806574013099311463018373907066109424905 n^{7}+1937682359609775750913320557610626035001798813944767022029292 n^{6}+382919013129438498442292575782607113307466667852096005649377362 n^{5}+42069455237330164621975607222947117416101238149158186951693000165 n^{4}+2775355976543432781556027725449314747762604992275686623435958689585 n^{3}+109949852809994064918602594222277723179316731747223065455893934604323 n^{2}+2422160299458436551606083335645322814339472454381869834197012790642548 n +22891291330334424839792866726809448343463426183493182079236643699280100\right) a \! \left(n +66\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{2048 \left(n +5\right) \left(47195543164745195883358398054202858835 n^{6}+2256636510843811547823375994859884952813 n^{5}+44215790367886613953516209486337058564593 n^{4}+454855556132255651290687901793353598805735 n^{3}+2593467919799152868148833935239719494621140 n^{2}+7777727355852916870137826966657559061330612 n +9592305392274797064106001432416437876349152\right) a \! \left(n +5\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(35307065582189626937130811588792104067194814060020698274327 n^{7}+16580768765114335021854446700637194021102279896207778648537736 n^{6}+3335958012646735876276869445522067946320216047266076320679657620 n^{5}+372740974662785574527438508284096397022469827478458016293636350070 n^{4}+24979358943995214769493362797284857204968545957222507199516944852853 n^{3}+1004005020030858731733419848928094552701415369181174481991698091333514 n^{2}+22409885988189201804283662108695530608519540062829007881125721176901720 n +214279371550683940953680968335974371412093596409512696286782180037105760\right) a \! \left(n +67\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(19378116734427446939423325727567198412152752627831651467133 n^{7}+9215070485702946790610855881131478583285450710918585318258928 n^{6}+1877685319804824757772111793274841583426077210375992600648749162 n^{5}+212513043446950469208297593569522564805561038508264587596203553725 n^{4}+14428059046626860795656645989566322659897298192944813985927257839827 n^{3}+587606745764272455713931498050599731146463090581230330357370300467007 n^{2}+13292150795850666873327547891742930514325505083532473447689592936498578 n +128832594615506166083478114814866153339177434107483771582008299582433480\right) a \! \left(n +68\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(13967557426608090935380834649763454327081022594013195225877 n^{7}+6761378715032700611867480952222936788189222109337199190199723 n^{6}+1402639980505939874367277256082858635737465491214136641747045411 n^{5}+161642882075265668230558608455534787604748819578262695557169406695 n^{4}+11176067783268181987511409904143477772050508250951039824524569731468 n^{3}+463598838975309985512310418275854597955460204403821490889444665547822 n^{2}+10682956682539314930470142434751683980225239118519999617485046285903804 n +105494720081953121067693253504096918990998258653165359758371177972826240\right) a \! \left(n +69\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(6651130276785826149937209898387781466041464237573457334970 n^{7}+3186429109029743033109568208818456718631800033867144066915421 n^{6}+653533480302718750788828020031366566759725114317825053400240181 n^{5}+74380986462268833586582509092480899630593943033671186778232801775 n^{4}+5073163869223590413133927224505594564278631557631716851715010598165 n^{3}+207340454990259073267970874738539189924268172954201856290025051631564 n^{2}+4701270578439789233728190477412381778146013598591428444594933339582164 n +45616873135424642576665740854600880160730775261190363795010459275769520\right) a \! \left(n +70\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(12933567852509099232647624615876563193786093902047551608189 n^{7}+6341424852551211375228791865805126459585891174876439433999546 n^{6}+1331877438910371345969634556937168680010723254006255012214788338 n^{5}+155327084227146201996056540182196130293954703799036374132931201260 n^{4}+10863036374553510714316004591090091198193192837248271078884664991761 n^{3}+455583215597756985666793583334546373132352122238919136199588457309714 n^{2}+10608735729281052685404873559449890842061108730544568202853307109168072 n +105809540599721318463197452541245721967100098228118799806505802370442880\right) a \! \left(n +71\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(11043299499481648490971428238826115993058726668685679420053 n^{7}+5507970886681742668072828960584775046871620003851823278971624 n^{6}+1176960848557489637928509238487961802992389522719670603694154154 n^{5}+139672313230879607693126143027003737012212600368120068564038078970 n^{4}+9941597601106606062048755688782715540635519622477311759447880597697 n^{3}+424419405863327282776716128630813978258879842364552839094186657226126 n^{2}+10062343970978176742414564246750582575234434464346807571637478994045776 n +102201877063289174777888194891377324884617022556541628109892188316163520\right) a \! \left(n +72\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(7421274105434340410461204702068181536825342121815512383956 n^{7}+3766740302931949620268293683133279320013779991525424208897257 n^{6}+819187315559304415738394105874757195044341487573252869399149749 n^{5}+98954009631699353450980986881007346456963425856894116210812592895 n^{4}+7170309818269863707061106527515734961591848268931335197261172099139 n^{3}+311669765373344532704914958839647697436330427204139740496307851162648 n^{2}+7524500979738439087039208481639852773401985804562392671857358962004836 n +77835989401128027372306204684508866375237657162219602664909183553872240\right) a \! \left(n +73\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(4287218676122879877896485891790186323658074559936251383163 n^{7}+2211974535961317304086024780184591944772940577496462430736858 n^{6}+489039348203817431842348455924918910263044185287744482244860980 n^{5}+60057836955072000022389594657494739750157060115082229179036179190 n^{4}+4424663255691967028289754762701987830899032936438140627638010202517 n^{3}+195557321732013699617595008986842376586798620540218489103731247421592 n^{2}+4800938395830876491367951340131577906759927787304250400429033256017220 n +50504572239855775996197794811868281986713374116758377870903583454679600\right) a \! \left(n +74\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(290989366576149349068484534416082937754432963626638639433 n^{7}+152323186830390929964467052193697240970036988727187946299677 n^{6}+34168829783904611155482325340032693933993460319899140015483247 n^{5}+4257678197285538634826420117733266237254243459427251575812748665 n^{4}+318285690184787842143971134943661693356509346719046331585353690012 n^{3}+14274538837319074717377600789079604329253311152087848442779740641098 n^{2}+355617498532620076054302120103734838646775422188027544062819609274748 n +3796426983936143573219150538267145357266292872785933577380609523462960\right) a \! \left(n +75\right)}{12071823628378784375000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(729098985803513994470008372637238318412977402290709327755 n^{7}+386592906332830692646206490589813595116714323471426807637743 n^{6}+87844510704918303715122864120748593477645297297823400818621793 n^{5}+11088502619472081890616248312721302565625606124658449733461948605 n^{4}+839754524852200664091100165361530714739353346125501517825964541940 n^{3}+38155124044205701959974699151631784753650737342995147687615198354452 n^{2}+963053905394350013946812983326701078298765240909078400254573240098592 n +10416963770301446218412511014652630786764454267731469659598844722596160\right) a \! \left(n +76\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(161248048014934070304215461144487767202521418915653382649 n^{7}+86337507324065341694531064978614662190922932696582408709896 n^{6}+19812272750838748534083199030033675908968070892613869407951834 n^{5}+2525835535695512807691668497478063450821922882524745983379201600 n^{4}+193213548490826396945187349244760871471448755693289608365255441081 n^{3}+8868167364007571219209690565371784253114350555730037139808308713064 n^{2}+226137372125701111058746586893120691149955555563773941979820929807636 n +2471444419060068507219010449638864093906208311741242016626368650920560\right) a \! \left(n +77\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(6493594531548673060760829306281705594062498070294396382 n^{7}+3829200739278022243752141048810579901058940942923139734939 n^{6}+960818881150579181167082549819063055125132517826137190830477 n^{5}+133114428164907040729793706895042239755745955966984548684471185 n^{4}+11005951514025892475258326961668940096505284611957128126047125233 n^{3}+543408534922690645222779804396020166270877554317846088070736855396 n^{2}+14843090509138000986583862626157115461624604807599664451187383392228 n +173102673511146013414247815979796890062982977284871581693642309235440\right) a \! \left(n +78\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(6727865594426968464315451230567080509333051145463762736 n^{7}+3753756560196900506073445524321566135364979595419631724456 n^{6}+897312342553892512975404911389338106914416958226891383393640 n^{5}+119128166272792371402790895555235643276836856429079421407049435 n^{4}+9486423069655999571639854164927706934485510288674244188956189254 n^{3}+453114383722221148230266996593483803197544381647721740080841161869 n^{2}+12020065020781313074660267484527161691312145009228836400141064585330 n +136613959205649433103578070980500030221215041847017653067131602424400\right) a \! \left(n +79\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(3786114251398286882124524599259332557992024497854887569 n^{7}+2131430211134450396022744207173018107886728540399207672812 n^{6}+514153833178668234101345133359262396368637789774782588742814 n^{5}+68891062977548052098056968955360932745756182615836376593648055 n^{4}+5537366834616757037860336971937084107944151908019075682411180051 n^{3}+267001249564930375496215619701490527812092703053760260708368862373 n^{2}+7151021804337144700734722941011360703431723460220794204053396702966 n +82065836932836081115295832937164179268813776316285272964917565039600\right) a \! \left(n +80\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(5318707777758502496417384950326011544154118637257624831 n^{7}+3024536537341026700013162963109657992368368252584885410186 n^{6}+737016524337912394903815871925711548107067268888757318745988 n^{5}+99761801327132150142681401740218476081213564608662398528121070 n^{4}+8101071487917670112743644110063518978213443839944983204553493129 n^{3}+394648515120682091584983106738991495019478612700163288585385873864 n^{2}+10679311417917467341226276260301432884706340512559631393137335457732 n +123832663558805672057158076571085084831645837256786912971295122223760\right) a \! \left(n +81\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(328925263225625844915810004382974453551417280952714515 n^{7}+189127826761621700145830275657512758070752376414080731487 n^{6}+46602325547609530861361633372234322393618660594009850823308 n^{5}+6379066274782515979922802931711273689424736895431656623859415 n^{4}+523874075164341496860789101101803501574918885003204284348108385 n^{3}+25811671358715296174050754841163933224806911816071832014921496298 n^{2}+706480519878167644413478947647640253847678526389594366627358762792 n +8286554835895181342343459684926229692877275603872017087142763030160\right) a \! \left(n +82\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(135537052893531827727372028693450944769827612997536931 n^{7}+79139060177669268254174152694741795282542943934085691407 n^{6}+19805593913106726279661016652776336147907040586641375478599 n^{5}+2753933288769717233063091503230105629517197570001919582666965 n^{4}+229779578988666647621792348124307914519462987931918229809754134 n^{3}+11504349238302018305080085693974761222681612588789913497284952268 n^{2}+320023364729530517116390338375528784333018703534911122311677172496 n +3815629348293008730840585857124764652551411757763970749015276925760\right) a \! \left(n +83\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(15875652674400457186179882134041197307046208947759801 n^{7}+9441462463066748776475696046942469232793279287957739273 n^{6}+2406840650033632022814133378968905851626176334750357681005 n^{5}+340925937852391451411822523493547722037347013062408141891530 n^{4}+28980177014004058202924225524112287817822047799511379296035324 n^{3}+1478325657667151152954054238843239845922349436525178394914916457 n^{2}+41902820464225472544252706370081093962378482571132948464523858770 n +509114920697329773787108526410656506699029977717324077853576137400\right) a \! \left(n +84\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(5473988933127520966366009332473232642274062542427935 n^{7}+3288028461972499200910870754070731159216013119480249704 n^{6}+846662156799518137982222993130611163644000520291460902992 n^{5}+121153576638454883774042631615313559792521361883565617931180 n^{4}+10404989184572029516541732122204732051291657722081193130143805 n^{3}+536327527019913522652523411857585615728899091034797646924298956 n^{2}+15363187135689482158626563633804664641030983656561628286142814308 n +188666255475625779280763865432847656016157116668411598750546402800\right) a \! \left(n +85\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(1938023627625487269468288837574841769308726770526698 n^{7}+1193187932936564254497589002278983162744561114782321369 n^{6}+314662973131811825037541531656337360896861328197724652725 n^{5}+46076220250430485632782683574466892576957018885413362837325 n^{4}+4046030649316209432778675419340545772476115393919805370795897 n^{3}+213061696683149717811377066686529854047108139381751286602011266 n^{2}+6229946616332680580539510996731122155173698582348409896037249120 n +78030456109673572317570808350514014038222438101263042006940209360\right) a \! \left(n +86\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(2071219194429929023693486146019286727608723534448241 n^{7}+1283581661140421056386978312042896611694800946479640088 n^{6}+340825418857454452061202663571319555237952398902342047556 n^{5}+50264056428739816072643152688595760411998672449193100239420 n^{4}+4446575010781475042467040011271163300827680397443320655709839 n^{3}+235959713618591201814333457793592206806922890080534028596802212 n^{2}+6954598081874672136793058497889203104380503614659949157234154004 n +87826453853650986614112440697953994031332211089052704458778295680\right) a \! \left(n +87\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(240304960308825825765897939259525047474328704431344 n^{7}+150606782325128185966336143474734574602171738660658534 n^{6}+40444665480464665188443865079280828686218303977722858912 n^{5}+6032801159916370820452813905943082088531282039865743802755 n^{4}+539812999629572658574707121323063995847043872126084223856836 n^{3}+28975832158759887383642975337522929607664824615088584297161721 n^{2}+863922143745283468537880370487621330102970020323288389265930078 n +11037143025984927946776600415766894890128997060333949407860985080\right) a \! \left(n +88\right)}{10562845674831436328125000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(328754767525167344662188158147899029913846976328287 n^{7}+208325176877558923900087320610963485983619607259265928 n^{6}+56568203858575257425050926236378572343111178714095606114 n^{5}+8532363800553367214050375536992428046630755846289015086660 n^{4}+772071521183606102599715188857765971150313677781590040818603 n^{3}+41911957897099526273553529211629773227651363201885907035582452 n^{2}+1263827708138797407149745842249119754568015142527230399531709876 n +16330670010789997203952774344798522947464811373544217518067765760\right) a \! \left(n +89\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(12220325558108928397961427942736160725599426673419 n^{7}+7814724747936912924565419339616045144953965405475251 n^{6}+2141543332877662950662212726513476665597383046659292829 n^{5}+326007161503259420308142038968246457037499131116142280215 n^{4}+29774110673370895468243752279304677411668974051120580973516 n^{3}+1631407178238374834558688408756668343333630700819951839773294 n^{2}+49656330055488744114930035050892880398104288444842845814280116 n +647696850607327613145925320760453393600652348381136931289771280\right) a \! \left(n +90\right)}{6035911814189392187500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(11770358961063769075278881868156203963857694739934 n^{7}+7552464905884228234345800518821637958982488442047563 n^{6}+2076525360348653947363277550589506327563679054180578473 n^{5}+317132259550780565645204551154277887010815294953595646695 n^{4}+29055133898102938862713659747920444705332233362589339363481 n^{3}+1596928534106571272489950623535065059234665472850901709336222 n^{2}+48753447609148808097526183895898267605104962852964411119638112 n +637791939740677163690954121628643229480747752168221952417985360\right) a \! \left(n +91\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(2051862975761521050644678784995882640763254024761 n^{7}+1369931774231209650727076029545533098692156523257538 n^{6}+391830485927728383356357305740195372186508933546300154 n^{5}+62237443441955153783745991854845424114373528182637321570 n^{4}+5929043801318481893155506612528701991874455258052820314889 n^{3}+338764960118539099728620112175277796037031863496410829852572 n^{2}+10749074660819047036575482184808540102299636609653847103754916 n +146116703823270949685171298264355232443143332609818194184541760\right) a \! \left(n +92\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(1664175244174658678504449364270931131720306310618 n^{7}+1107769904920089960672515222852826769261940868045737 n^{6}+315997953743741887421906305560799828043063595362625333 n^{5}+50073325605194328204707333181514922114922077963250598865 n^{4}+4760349607666008973259194002091332314205150871829783480097 n^{3}+271506731734784590784724252405144998041248742405468296567158 n^{2}+8602151457533521157921013998344515045920799513979807698110352 n +116792032258691490591849342354751258517303205862908707764737840\right) a \! \left(n +93\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{3 \left(80212040411508378631613611118231338315343541612 n^{7}+53765152258668689531202768704816121890459004518674 n^{6}+15444141846556649814352459828551012961501140084362353 n^{5}+2464516572875669588205289419375508997322963627848835960 n^{4}+235954210618596620711786434294400381352748300183919377643 n^{3}+13553484995709733438468176467065266944868483038386355099846 n^{2}+432490905514702838123390374399967419135648579851118692843912 n +5914264170218765607266555928523663757878732726583381419896720\right) a \! \left(n +94\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{3 \left(13441596351163548086720847411866147917534722887 n^{7}+9053871180871523831445057712141031449648045742732 n^{6}+2613586179579076857666750022448529074594800139313492 n^{5}+419142466235719610735264650845228263320882814795146440 n^{4}+40330310445898759197213036699574289190047402700036178333 n^{3}+2328335148595363784143011715769827811318168104225233086068 n^{2}+74675588265462579389812097890431930512514314088599069352168 n +1026421412756247536229909555281214962188058130859422405531720\right) a \! \left(n +95\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(5168240167739369672838845783776564372140230824 n^{7}+3444927794278456395164446894156564447109982702129 n^{6}+983562670024136852221606731620671048523711255846779 n^{5}+155919665992942418134854152123567504817770738504149635 n^{4}+14821347306049143615058661345993664760325783719087829881 n^{3}+844789634098699567188783313676767496232061516028531564556 n^{2}+26732823071424290321397410924438025043263629496461718380436 n +362289595701150851879005995175833996052633656967048938255600\right) a \! \left(n +96\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(3419198940246239397203 n^{4}+1535925645904442263906504 n^{3}+258704371035034583438490259 n^{2}+19364710292138286618733193654 n +543507306186325026349329799056\right) a \! \left(n +114\right)}{1379636986100432500 \left(2 n +233\right) \left(2 n +231\right) \left(n +117\right) \left(n +116\right)}-\frac{\left(1810475258120012511112213942943973959 n^{7}+1363945464514935809110792272544811445262 n^{6}+440169900199501310104001952288113355226640 n^{5}+78880894491961666584832110585085284876099130 n^{4}+8477735269220971441401400256670904018896994901 n^{3}+546447889859637895564129273681818257558895264568 n^{2}+19559549322820892965779569416573381464278765350020 n +299922917137089148506511833407796208047060677389200\right) a \! \left(n +107\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(47517420321669864131285447230801521 n^{7}+36052519142458659855339712850118215798 n^{6}+11720306292910418156711091528519345175806 n^{5}+2116259765765710741041246951730625329415600 n^{4}+229219279921084301329826149507997661105260529 n^{3}+14893169406838344757800019556532407499482116442 n^{2}+537470674941945441745111162171440768502053591984 n +8310962656456480708739157272863804150869443081520\right) a \! \left(n +108\right)}{2112569134966287265625000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(1190941247165862094640863847178757 n^{7}+925886128783436772688990393529823756 n^{6}+308254853218687827610915552628366210614 n^{5}+56972832618938724878674859489735108557836 n^{4}+6313496265532422385959590448576151849818817 n^{3}+419498180960767613058405873521372057278897080 n^{2}+15475237625312405213559796781929623899726978340 n +244511492567231366501727530119948561884306056400\right) a \! \left(n +109\right)}{845027653986514906250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(14618882988911753206931054466981 n^{7}+10938844545738345053715434084997575 n^{6}+3506231550357513354914159707873270503 n^{5}+624047367739748654100813491944323375065 n^{4}+66606590874886427906926992068929295040324 n^{3}+4263144598293991966220450307980125189865000 n^{2}+151503353268445939388227545460487843757273192 n +2306102649578119119119857132467679483762509120\right) a \! \left(n +110\right)}{84502765398651490625000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(193062501280080635106224976147 n^{7}+147862133145963855920231541830674 n^{6}+48528601519032026478628021306940841 n^{5}+8847572812201541667580854437753644099 n^{4}+967741419308030405955691796570099822586 n^{3}+63504253390882438509788053051509581817187 n^{2}+2314889793618944251767686637706589961143106 n +36160716560255941106724265994532546421341360\right) a \! \left(n +111\right)}{8450276539865149062500 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{3 \left(8264727832196457482107637784427809514972912196843 n^{7}+726976927957404938802948527380339428976113096647408 n^{6}+14671192659358615220916554324871583112890101836160098 n^{5}-598100019876885442500345196743386054125526341474667010 n^{4}-36506986026480812955791498138532779795614411533044981933 n^{3}-770608942942431841563395549421982545008884522735653383558 n^{2}-7636780728828592980893997271284281453820320548319969838008 n -29851771649712995896947877129657170907532535773867037277920\right) a \! \left(n +19\right)}{2640711418707859082031250 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(37767679527810954342111525746903143068586764522469 n^{7}+4862681628740387655985912703231094882994215446630306 n^{6}+246415257899028587582006490048502254296622040983470140 n^{5}+5653274612285029398631171858767173758524969596325687230 n^{4}+31654995566921349966293627057729513031430363377056462851 n^{3}-1089784006645397435599519224491205076136318033415955985296 n^{2}-21362237602163862429059583407154391441266580398864368839620 n -116955360353698271850134399365957008571212744142263847492560\right) a \! \left(n +20\right)}{5281422837415718164062500 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(3553192853446790960271490120521306417887528429050683 n^{7}+532800539828892975716341132738804311578983909947942625 n^{6}+34117329727496501897212546181797598196193989252621602277 n^{5}+1210334738171227511920942714256196114917380496027413804795 n^{4}+25715000513545920363728414641019823589062617979280710436872 n^{3}+327563237819821133573133349100865905665552897613395911698860 n^{2}+2319355493735526376530662536556623230491985680749051332187248 n +7052587242274701028266424791292500094751107386140978267092320\right) a \! \left(n +21\right)}{10562845674831436328125000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(2688315867956812905366112535730227737954776880401 n^{7}+316634830878755941634674425334195507283745178508114 n^{6}+16123569214892967956003096696016168229281100204638912 n^{5}+460807873848729684943208986134620049393376508091098810 n^{4}+7992322907602479602088417557564651019508925438339037699 n^{3}+84188995942427701565277861649690553426447505844999463156 n^{2}+498827981833064407508899927313612661552026110433354689548 n +1282090788446849650391630085801189808439420064532445487360\right) a \! \left(n +16\right)}{1320355709353929541015625 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(22131005072350598850963344106820425745510498289151 n^{7}+2947457926559477669103030925512967136093310989624203 n^{6}+169083620697242461015101808646932569325119829743389007 n^{5}+5415310868904647993500309370194354802151704867315568505 n^{4}+104554421393127915740303092345911922836681833552922300714 n^{3}+1216507504640859315273937726769979018660174258940897759612 n^{2}+7894605434952979466992321348243914500259169357329611892168 n +22032618632980275533047609199412875848606714361749106414400\right) a \! \left(n +17\right)}{2640711418707859082031250 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(4875930398463241459981335401153297381517731912536 n^{7}+748183337368655015849870691975373622699690193244779 n^{6}+48969846340027518270232755191196780621635267108268943 n^{5}+1773667170673654681345579347906353774494092554966293695 n^{4}+38414694711279661385022557091495657710805611949888216409 n^{3}+497688742495164504142859373331168659886994176011360767046 n^{2}+3572106251159557025674027818447939422387709605810023445712 n +10958392759110955632667247774444220441710059659940292697600\right) a \! \left(n +18\right)}{377244488386837011718750 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{8 \left(800488619340207597394793956060653982149685884 n^{7}+129863288016873264574541289030031991396150152633 n^{6}+7393908358283750222427460426756951896250202833353 n^{5}+212904545302166949634677428486352231534232347445735 n^{4}+3481395696715717539292954537113483859360630926567591 n^{3}+32939283372810197220689597164116407405052113889647872 n^{2}+168729250030465819941126269372450770924625866705497252 n +363311574494448666112881368215958462433392044695149040\right) a \! \left(n +12\right)}{1320355709353929541015625 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{4 \left(2325424338604188856975172656042663848365267840 n^{7}-38979947401508643591117937817007844269143153549 n^{6}-13908734949799893181502055405016274380656324229795 n^{5}-635604182702015790105209787433722275605046669962175 n^{4}-13598856566136740569138600122282026099710299110249065 n^{3}-156609000063068593345407211766957243892291439338183116 n^{2}-942079375103453403532530690479357514383812338245598300 n -2333458134608964522760210035941564967778736724459145920\right) a \! \left(n +13\right)}{1320355709353929541015625 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{2 \left(29814078088989561666645421477706643710878090439 n^{7}+3012079614229107091271894306645804187658519467571 n^{6}+123666461743947603800605117115892778090624640107199 n^{5}+2624591072586545214379269078253393901076829887048625 n^{4}+29711279395694206473351671438044936299427783574241266 n^{3}+155721471253102443316517467140898039462482080512976764 n^{2}+91994465509007585205502408369396023297732903647112936 n -1557993489544727267131678012370795523442749287711230080\right) a \! \left(n +14\right)}{1320355709353929541015625 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{2 \left(90755010816344258137874113898348940783353252208 n^{7}+7471854589046676332209788002966911346511870954625 n^{6}+246806374746642264598866852812205285557477955526605 n^{5}+4123828418499529159924530997216739606560184856303745 n^{4}+36064138730359861601577292335486505989621107731868187 n^{3}+159181737670110820917608924464783262915595489317679550 n^{2}+438535980706379800161632308569934718995051613847650760 n +1525663978028843444738086390772785675929143775974861280\right) a \! \left(n +15\right)}{1320355709353929541015625 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{192 \left(1088917975617063283532037176940177510764575 n^{7}+93098355469809646500731792232964730654490503 n^{6}+3411215599531002009909481189663105325180641893 n^{5}+69019375077856787841927689125068449069268219345 n^{4}+830208138743977281766693519316402874036451276700 n^{3}+5928764466814711960996347276647594505905091743632 n^{2}+23266226830939010951899581026279499341002631584392 n +38712581959814069556676882626952433813088966327360\right) a \! \left(n +9\right)}{1320355709353929541015625 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{64 \left(6091834228757295177100330603601528254491913 n^{7}+580031157661798587052380714457881288295008244 n^{6}+22111228287193880495678887500039446772618242611 n^{5}+447062455422173718685218814001070270442066909495 n^{4}+5236698412332837086520051104513382638766122961982 n^{3}+35762841226436917179428442007174916204378191382821 n^{2}+132311639812667889316655710759658023247315869613934 n +204916118800949435718544619655791703789350346787320\right) a \! \left(n +10\right)}{1320355709353929541015625 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{16 \left(29475096313911191292675202610720208258823233 n^{7}+3361385037303517416035447556937404829263065813 n^{6}+153223452135896525534792266911374092039946821761 n^{5}+3714753914275928791548862164176954338654963252595 n^{4}+52446467093735157595753580606716197271620497761302 n^{3}+434719421638584683196072548248092678410776112369552 n^{2}+1968999641045553442454838568905036023583464842424784 n +3772759440379344555102209323257342000349938164777280\right) a \! \left(n +11\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{2048 \left(345257886085869008345530537552747679890 n^{7}+20971023160304175824549975955917863685148 n^{6}+538244357635142780448207123170303454735997 n^{5}+7571053007248274935622033138240478079190310 n^{4}+63076885032624698310474425776932482859681625 n^{3}+311483655842910835686218120415234938831402022 n^{2}+844763176750575803092736927182395293198995968 n +971304100458308179860352618801110057267625920\right) a \! \left(n +6\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{256 \left(16174119258918989903995367535864369091919 n^{7}+1104193718473771715216474294187973675565429 n^{6}+31953251823034914465781941941186337054914843 n^{5}+507974204446543706417370699060248693103507455 n^{4}+4792229890824337273653639293971874568262115486 n^{3}+26840024976285117909294341468315532646217689436 n^{2}+82674922002098523627962352645675186715161971592 n +108103117526806996801110709029881309851230632640\right) a \! \left(n +7\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{128 \left(127190551825712653183604382939953765801755 n^{7}+9685493846057579707054152762009874273420920 n^{6}+313519691389158538660729767952771391682534454 n^{5}+5585568160041655221622431825061786570062002160 n^{4}+59125658683345214805490691874371326661144632555 n^{3}+371886038823078787990184013701138617556543743080 n^{2}+1287273381094661209333433934924753277134878067636 n +1892487715470504290314531648995040125163090219680\right) a \! \left(n +8\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(193469764621020337893630536460562308750393 n^{7}+137768902283879338521677848309473312095306090 n^{6}+42057751429308506911740300350099957883784118646 n^{5}+7135192955604084342678338892751363816907698229390 n^{4}+726536969778181506053947783493144277883692832032117 n^{3}+44402328064636874684045665431715896100328778664743800 n^{2}+1508098416625419837705044510628128976098249910795554124 n +21959823708148849710136011863706679398226070930541336480\right) a \! \left(n +102\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(19895270063625028010845439804955039367154 n^{7}+14485233221825352481745100777443985042767101 n^{6}+4520550256085592286595924392410273052043506601 n^{5}+783887505332589384748651572056969202183446600605 n^{4}+81571545481795029596828691731154348464549110480301 n^{3}+5093873961644309375648467084014387406400051715875974 n^{2}+176750426273857253978772090774782905291387772486334264 n +2628894306643207461664145080773789080108177401613290560\right) a \! \left(n +103\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(44713048538930108368725434663917770920 n^{7}+9746489928868824809746323841904432193933 n^{6}-4110213914219308291799595330725057939721484 n^{5}-1958676070303318237345248063360755967167582145 n^{4}-334057693012564987055073006491520116687038049980 n^{3}-29029042822091705915767184604758540976736532502828 n^{2}-1291877395029212199058217257036074700526741155081056 n -23464721802087755404864231145086357754432931429454080\right) a \! \left(n +104\right)}{10562845674831436328125000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(94637668861891325590248914554534049569 n^{7}+67237874892927193420256114828175397808764 n^{6}+20444879497774208017987602524141298108739414 n^{5}+3448494518765703778923215388495358678326123580 n^{4}+348430202752735449393336168340756305061441323241 n^{3}+21085257421281155901637492827725152779035617944856 n^{2}+707492475796796099666805458138825853553196958819576 n +10152111147630639498798637654146354791100008190308280\right) a \! \left(n +105\right)}{10562845674831436328125000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(14529935483950239328279374990608294462 n^{7}+10640475441476478353208692258683734527653 n^{6}+3337655515528727377200674165286569228658203 n^{5}+581300064894659112258966855768619712175496435 n^{4}+60708801441495448398490929914392260405324721763 n^{3}+3801761834446096499922754818349605994760997976792 n^{2}+132179793215261889964728404708346907080420903114372 n +1968229178267458771156702973858777087457709074222960\right) a \! \left(n +106\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(120100478305910089934217693255243566656410 n^{7}+81170338446536576485680732583569811782520045 n^{6}+23453009813463718998642687038897159780301383208 n^{5}+3754446397596104055615426873285983761005998718550 n^{4}+359532527014997761362614172415123198335797509682460 n^{3}+20588664926007402156041117652356689308926343157365985 n^{2}+652554816926818493643142083817946090397593890824964662 n +8826527206649075471691256664409453892140402881323236720\right) a \! \left(n +100\right)}{1508977953547348046875000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(630271989540275176790604893620676944543361 n^{7}+445911484030465725843513838358352396010722841 n^{6}+135298992157444950335092359972026713938827333687 n^{5}+22822971553547124455297087276433041419099434845935 n^{4}+2311569342533035507018366415737924265647996063341224 n^{3}+140572327301811663755466561064128697674992433239773384 n^{2}+4752560439792612895296058170065576850632301909446881728 n +68910594639772006811488216463134158113560787577930454320\right) a \! \left(n +101\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(1375502441936970545995733701308383405159402411 n^{7}+954956303529758617976922644523153818143057784734 n^{6}+284212232401544234983172396519222262645675516459932 n^{5}+47004148084266154534904167225519652055509015901259810 n^{4}+4665309598300519824671070909751481336478659023229143109 n^{3}+277887359572470590598693716631313063760051082487795482016 n^{2}+9197521241340892904971912461485122473764799077423529021828 n +130489582951939441547700854374488176200502535370610028462000\right) a \! \left(n +97\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(230926539457524981765538874796159091843343124 n^{7}+159240105162268186066388928625466145304522648039 n^{6}+47074933945918318943767337729614319710022331551187 n^{5}+7733740916488117745852149332962463488275796188952695 n^{4}+762562553592244560905050059830631148293001251367412601 n^{3}+45128065642878297686269373549291525480796986564206807546 n^{2}+1484153747546142202637878439489653157444497293500421640248 n +20925068511917810035542195405675824700426623266707269064720\right) a \! \left(n +98\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(65739096938753028431371310162915912154586397 n^{7}+45194548877052166563318974529239202241034684032 n^{6}+13315452400529232716019237813372985884280370583698 n^{5}+2179406880796350808282591611556120493704572627883360 n^{4}+214021634735662825654869733388630104070224283728965293 n^{3}+12609988653318126204197575488512437399393253383887007888 n^{2}+412749265549906920774501689834204124520342357785522397572 n +5789871499953155942811333999207845126640510534656010233520\right) a \! \left(n +99\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{24576 \left(n +3\right) \left(n +4\right) \left(n +5\right) \left(10150753270258609262101463753492781 n^{4}+250131616257425147474750354629381549 n^{3}+2245146328126095006752383693960917100 n^{2}+8654646837125292721520152052569486620 n +11980425504251960298946082612146806816\right) a \! \left(n +3\right)}{37724448838683701171875 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{4096 \left(n +4\right) \left(n +5\right) \left(2898693872071594625572216355267433002 n^{5}+102946815085170430307911599171941450177 n^{4}+1434588664658998938915338453310089933086 n^{3}+9806621571278062120254218425287478002871 n^{2}+32878203599700724664398972015289357648244 n +43223135529236752333669591438603064313084\right) a \! \left(n +4\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{38639944172197640852832718467366912 n \left(2 n +1\right) \left(n +5\right) \left(n +4\right) \left(n +3\right) \left(n +2\right) \left(n +1\right) a \! \left(n \right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(22426853524926215855438745072327458568385610132714727 n^{7}+4550927123321284828633016832186353325805892977225082600 n^{6}+388381278709200563138493174339278321968653789113298938460 n^{5}+18155697587497561681779136643049063573746274849339506545670 n^{4}+503750027118681494958345610851097219409496530057089842698493 n^{3}+8315611495453752830753711324348238461981573657491463522718170 n^{2}+75751942224005462540347847433921554570474075674561995293896200 n +294168548315230067211012499534832978596243296890344849413735360\right) a \! \left(n +24\right)}{10562845674831436328125000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(12793517187120920656263104749233424603185050238654481 n^{7}+2043325873099999763237322228315985983374745908805419784 n^{6}+139364216442209666640876269370337359406037169778719778012 n^{5}+5263413384890868123859798221937466201290605759271191857190 n^{4}+118917636566732134999273877323409575262676441586799912569579 n^{3}+1607802404409547643203282508940422049778236160194062330114346 n^{2}+12049294536522387009476850912116762737860189598765771368016368 n +38628350075219521139720348599450074676446212484394991081538720\right) a \! \left(n +22\right)}{10562845674831436328125000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(1388228947633993601806212142860142733779548669181831 n^{7}+241670359377002303047040107052213238345854535190543857 n^{6}+17947091357245344856816695645293701953942354802539388576 n^{5}+737501966093103384640729803580236703319602839017337045375 n^{4}+18122263262677816927929179456609817917248273866311770218829 n^{3}+266428001548046132317847200086955419124669262377860839183148 n^{2}+2171029600618001199332401302789255115994964335265545028433344 n +7567984195197686327627301393658081560917038491323746551149760\right) a \! \left(n +23\right)}{754488976773674023437500 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(58875458726428345638096648987817194858427380540491541455537 n^{7}+24139459259057269015594810694107870618976111710443352418874013 n^{6}+4240313550880633348841807448933785759934418388550553778981905847 n^{5}+413671402741652614700409224328900206236669539886057283558746850275 n^{4}+24206359964464330023234768961652721056702990972403109259568715957088 n^{3}+849621642813386944243601880243084383857903975360523391806649230658592 n^{2}+16562490656198323741111936714326331673857962751233917824114481634649128 n +138334708157222798316171262754017598235635849005816988435706280505329920\right) a \! \left(n +58\right)}{12071823628378784375000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(33454586575681617470437315782954074155675228817682739379449 n^{7}+18442507574286536920977070665900837257826527650383493788215831 n^{6}+4072369824293323695910052304174974923337064265875003467914593283 n^{5}+478845574764495502295764278758726533607393985702319063420179124085 n^{4}+32814181268623751546566336172938134264954926474841672119123541927676 n^{3}+1320883528616343107745555801301271879115850371376075974603003405565364 n^{2}+29065240736288881718300004642498360064521962249092145257937144219717832 n +270630819697614352196407265818872946019613544252101464864262975094540320\right) a \! 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\left(n +61\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{3 \left(72214581485420141577593667440862924359560412303291818139848 n^{7}+29456146612233030433274351770682940737497102582050799141903663 n^{6}+5142316678998578645141378543254709836084193213772955329190061701 n^{5}+498095603284903130282748691892517214592212265977829228647174097325 n^{4}+28913003464611029940549109345878849146535981945025445776962421910607 n^{3}+1005841352133056565305908579743427158201011206900152592182871325185892 n^{2}+19418897328705953838981412310538276500946053864562213187903162676278564 n +160508785040243063502097884797851004746563154351509085888934102405242560\right) a \! \left(n +55\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(118001495490208615318959085374619589281526122617831920834177 n^{7}+42414741955756868814969020662987100605041589755674694318889031 n^{6}+6460736259264600643974135356255504314489675676699610662039664905 n^{5}+539066775851512024452990523220922181637336802972971196799788486155 n^{4}+26499359305764213976338832857860098507223841599141901238982971540538 n^{3}+762714966568615242197070335666336856424420539157946032993474653865454 n^{2}+11782588218088107155958014931768004267938092890464024003462877414782300 n +74032582229648498733752662512285703318700579391495414824610513323719680\right) a \! \left(n +56\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(443732579590059085627758028963272146466399532700361439674150 n^{7}+175874677139645025044833346576835986923054170663816906938504803 n^{6}+29861751970381372804164433126256336542130089969558504907697694749 n^{5}+2815492392111594672412368586028981066292815101693696394486707853215 n^{4}+159197683711612606689623279024606414304754370833958676158665718112765 n^{3}+5398268323078377896046858906548174534181358111374297483700800833863942 n^{2}+101642498250396156862445720491093500872547071629519856502677260137358296 n +819758840811863301591391397581107044128261207083128827153758711637766160\right) a \! \left(n +57\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(110104560478009738232414227751142280168899392631481362887041 n^{7}+37207147868231872015140260275143258513954206716449823654025943 n^{6}+5355044876808123965705422251306589726215234488526049662457625263 n^{5}+424963093589743497859500031406618244046640385467466422437915983345 n^{4}+20047749718104548834529177373387984425755784195659457452679658075384 n^{3}+560909617459102827403563484453582521627728186140043748330124730764872 n^{2}+8589943915633631496554780119031180643295180225862369647342097175358872 n +55281555296584908277006890543816860792714941056107659689899744260538400\right) a \! 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\left(n +50\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(13456422794820374530503091197275397084674141011115946801433 n^{7}+5054017162062581792335318533906418640184132110619614577439738 n^{6}+812907925215744480567496355185746869375441118015902641884004630 n^{5}+72596414149390389813902767592295062415131702589761806829233892650 n^{4}+3888118817630211878642186989027568787532192345035586517506147256677 n^{3}+124900331224965208647272266085355315306478018429802053380230940776452 n^{2}+2228462469670722639640433217543971565906071428165914759291231548986020 n +17037098020428640553570525398663679988107107094763147137447856456619920\right) a \! \left(n +51\right)}{12071823628378784375000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(1015906445676972556007182772388906669467441709962993822137 n^{7}+273456519341108705149238493318504753581625434505976734333472 n^{6}+31218102695838691928973231218475341737075728110404184578761166 n^{5}+1953365566753315357696708925278157878181660976808087507448080630 n^{4}+72001696986963977818412983950337369178199711299565689584916096233 n^{3}+1550928240255284155479646725796986245549427871950653044053199043458 n^{2}+17817892805138745218937447456264291025804383562912512341218041047064 n +81822766898094520098687466064736737367651159293841765032120263041120\right) a \! \left(n +45\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(59321363085278292980851857713571613547749688417164942527416 n^{7}+19708570318118201977954264321763958625139282746591039040994947 n^{6}+2808034884786449156404058458214615495398726023846435243344811155 n^{5}+222389997066062203748692673895872790542388789445864867311208032245 n^{4}+10572488491417381790376447630691820271482987842527916361561203211369 n^{3}+301683079476023753647649313906790329737432669444396097813260074347128 n^{2}+4783851492996982427834504528078490380364134256626725115097581186843340 n +32517758078596764791720615706103628245630383627524497389849239738637840\right) a \! \left(n +46\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(1458126359763555288565718584675545702787393438559854618094 n^{7}+517742757902207349585169544566533246258644276738246791539449 n^{6}+77322181240702894181398515058948245116888195140052832960325835 n^{5}+6320346481478045908161726219611924663746785054922912881255860465 n^{4}+306222425181503095734373911591259191165842260412204769035964691511 n^{3}+8811916623980374420542087436424220070453186644910435900039761678566 n^{2}+139664353647470778095579568241232746108603035868543363210682915686560 n +941672273363749105801386775043518114114243319942426394478423917820560\right) a \! \left(n +42\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(14568725011007927047210880014028768047587392242653484046833 n^{7}+4490061731348764274622154164639863647150876212192955062346255 n^{6}+594522901144255938132813865663324011862966670487155197248143725 n^{5}+43834250992801571886420678353871646759609270732078635100178862685 n^{4}+1943326527006568545696124217118291711508001747712295536871210973602 n^{3}+51796089212469501426627741626420848093977291750161724274662012967540 n^{2}+768375661322934948358842643431982652641949553901934886629218569291600 n +4893291844169917699923017998426825962202902524826639450846058430304000\right) a \! \left(n +43\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(12613636633926828118916962313550579048909857328536541367067 n^{7}+4057092272834797117813764308136691551207300836210631644613299 n^{6}+559779511661668186430258115587358390813184806570143281371698114 n^{5}+42942895796276029564975067224149359339974662913365144368025351440 n^{4}+1977906881156624065022351092307144686358239574523255646415289485273 n^{3}+54690099606219175830932089158941253985182452250996816812469297261761 n^{2}+840481884676189641739359180873604418197890114449796693910637832908886 n +5537536628708420707321589947403974813130566446097891139754700402467960\right) a \! \left(n +44\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{3 \left(3438337965961961438957356163757783716765630575593294657 n^{7}+1076974955517216869920564547232705266219187963540726168293 n^{6}+135894341085572301084679091724242053635200291819200679816387 n^{5}+9090435101935952184816885894188389142939306258150306245041325 n^{4}+350403220888874944750215567522413417602039506466170957234704208 n^{3}+7791005706529490156187105108013499726708436637727763428314454622 n^{2}+92157674268894582646756703389255504119502780962433895775763411708 n +442618753885463119977645555794030913783446006561305617997557436800\right) a \! \left(n +38\right)}{12071823628378784375000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(528436676200953992767408884571943432750316753861271091348 n^{7}+136956242033744147049714703172485390405058051931142973421544 n^{6}+15260027041044652716652736101267699550645878232254943476879511 n^{5}+948672493173016763312441512668198101877623642066207278952447440 n^{4}+35583835047480200699024016810206429580610172815894893727195834697 n^{3}+806450877599736402499606482884739815381941673606225782413288354736 n^{2}+10240053210078258773614922410564016752278280925561975653177517019684 n +56277651441791825577384871133061624707021487428653537929598049480400\right) a \! \left(n +39\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(2297580065300325548558319132480641096931529973656569257549 n^{7}+624346048160685723490276331562802497605569375230735311593193 n^{6}+72520043006531309390981124981792134855927527424844725394865943 n^{5}+4666203436460448789039149327154307525365403027604752553477893865 n^{4}+179572596858143989001143856982188806505829377549459581109177620256 n^{3}+4131815192759467015081794505318760138795548053517222812267269493902 n^{2}+52610276065366097580717396678307524731260223294588124396065030234172 n +285838644097101223891327227062537499886321216267384430155313174223360\right) a \! \left(n +40\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(7256210889131274053986215514180533778550594968182351481313 n^{7}+2129479655848296064306946735379184911766861939902081674824739 n^{6}+268322413386395838050930604831074808021580452516580212672576587 n^{5}+18817691000272206155980708226529046678422137580034779425848719575 n^{4}+793273338113682258529556069596752634826276048423473612710847941992 n^{3}+20101093684883556100754192196445972024197597004575891933636007445846 n^{2}+283479741104878822308468001451395930962201075569562272653930362366348 n +1716368495209749161884588532963325696568651589177322579873931799508240\right) a \! \left(n +41\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(15919923898908503745597752914993528900540898083555384668 n^{7}+3684035385375118326066333782327878383782756572248079332410 n^{6}+366088256338717222322863393160301682830610293036357414253275 n^{5}+20253871676008603261207285364691428153020566184884278446297550 n^{4}+673893319023812146920298477644616067898040672168241337996888417 n^{3}+13486853375190428836059839635739948397211411599428510397786899060 n^{2}+150354177803712427147424951783529970105758418466506332091579184580 n +720393450946914718573173416877630788787525801436744766769823864080\right) a \! \left(n +33\right)}{6035911814189392187500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(121408443313694785672778661020203262903057307016186072955 n^{7}+24322505153323739986698233059405101555010437010736857409544 n^{6}+2008489031807761666348834555406767963791362133843905547803828 n^{5}+86759416801204450772938342281514613312517521697563651865071070 n^{4}+2022297985132686575816795620973652241421654264976798489610902785 n^{3}+22223531308576922632192913823450155568102955654611897221792892666 n^{2}+35512289988029538042838527759084791332719019358062787969504029392 n -878500770140923571388270403180739624306773897205186537895675442560\right) a \! \left(n +34\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(99645980050695113823616069767805035915690781201477490275 n^{7}+35780769907048683203701891841491689610461390756083463376170 n^{6}+5002426098310741861503418034859326548129164167899756075184608 n^{5}+367566451720041484145069371952838694252430909369895792848099940 n^{4}+15628036504657870756216998006399955740048020151566686408489764925 n^{3}+388623142240490593050433188730599729743919232063721817935179519290 n^{2}+5267812077737295702564299132331542961059375749742131383635372625672 n +30156123145772159212920328468744075408099826180714203201643869786560\right) a \! \left(n +35\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(683735361968032337885093169256725428859298617214754438011 n^{7}+171715875661982867174708631567711499866621180680855896579181 n^{6}+18463339621786303878631636805819394393657402572208205927453111 n^{5}+1101551764570466147839081679192159147281587570524711398265329715 n^{4}+39375256408662498676082063138554283249409074781483839731144253734 n^{3}+843065556887167025776847929063609169317196919644782409003946981104 n^{2}+10008729055644262203164683922388079648605787074580570109612690346264 n +50809086983725719781124887300569690001833867934936538476006444047840\right) a \! \left(n +36\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(1513389928535262414549884112488984319343896771885139148093 n^{7}+407267735054277285698169081086280783516519188718154035252798 n^{6}+46969648912713805733070805321647746219536775498772084561020204 n^{5}+3008902635585696214095191824753842908983355994023247889769031630 n^{4}+115617344464960095582534076048143218089192125323106897811433276387 n^{3}+2664487678228605454204754079134403536203493655446100216126876159132 n^{2}+34096739731912080134894982136060522640445412609633858640200683488316 n +186885793192311859469919791613509352029159773942469833643424795195360\right) a \! \left(n +37\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(1547817500756858519386904235376574945927654414540600273 n^{7}+328980707577633492095710912746885481469798051185560550018 n^{6}+29534771540561274130168167515243440747615698798527544471434 n^{5}+1454358075527640001187112151292826454418245684367991438029260 n^{4}+42474082331429636364454841886724065525709889642110151587471037 n^{3}+736260779575088188244993468923707497855328505974930079559573842 n^{2}+7017346390318909873718426060174380513820505906366127432384750536 n +28374651653248534916471812204843186174776528088284053437622758080\right) a \! \left(n +28\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(10083872595625738183505749667535407719992063630126541358 n^{7}+2187796450275268221774376909216723870443052534038509840471 n^{6}+202366051219047109297757538625138085390657699420274801789695 n^{5}+10348382187776387980859489975232940548023147011842139790931185 n^{4}+316044479516929108873322829870224956885031822177841386237448167 n^{3}+5765653316961554894753932666670841661275897128438508078326292824 n^{2}+58184591061703203672045943436656686996020962578278262643829707980 n +250586845934548504132929776819227911644274188332937176386334078080\right) a \! \left(n +29\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{3 \left(12607278875149476466024880757315448796340401238690852759 n^{7}+2919148695731723426764170687092922691093149040395234564083 n^{6}+288065099140620359472810918434482249720756571364376300448887 n^{5}+15715331757715413775452316372256426454391256436964770751980025 n^{4}+512170841417603899603684865398224219828031799196265202291429306 n^{3}+9975997280420074246004900511683696280642664742914907514627635412 n^{2}+107567688399583121303606773159090167090712429457514619928370549048 n +495470795804891176952841482834868254038841735025403905605376842880\right) a \! \left(n +30\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(23476936955554593541420568621078812447264962650131846812 n^{7}+6295907088370497443897377710363384699359708848643549053943 n^{6}+705428364992066885311560066286724967461046012200509306013871 n^{5}+43087604571950454307906194951046225300543740472232289506242055 n^{4}+1556079893302067120694699557572266670031871752479439291254607133 n^{3}+33325072223086554402968819950266522094545630103246327062150185762 n^{2}+392705742484279893487967370619018325862749161450582486119623647224 n +1967438437922342025407199853253832350565499672842980921435112688320\right) a \! \left(n +31\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(76271474149086841380561142548698807456948147124170766154 n^{7}+16581827662093590135467835721316170345737696080695470671977 n^{6}+1539091733264323810567892204450944431230842385210617852937755 n^{5}+79020425702158692598159253040479790371356378108689951609502645 n^{4}+2422226242743768948656697308290080798535039446699624304686677971 n^{3}+44296401263106755659689630739970314853945836929708222678875313178 n^{2}+447074336957527519703201830860931263603669330074432814391001892960 n +1918866410714621311772804925502930357125905087341948214838249666240\right) a \! \left(n +32\right)}{84502765398651490625000000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}+\frac{\left(28163271810462625122998780499836250780392656394155107 n^{7}+6804098389808326978468033226915409458120655241661466181 n^{6}+664525769567736445981760725886103676158665046353925401703 n^{5}+34765272201189716408150306547925079793044317647663054951535 n^{4}+1064721319881137679264014995803353450197963434066803016836718 n^{3}+19224700904729962069673795267703878293479252386465167264515004 n^{2}+190357425529633371634090363053643187724708440196018498387968472 n +799831366503087085159342641342973184872825164462039688551987360\right) a \! \left(n +25\right)}{10562845674831436328125000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(113531910498279230923774074838333849112807898616633237 n^{7}+15345438784664759552622566708324114921255028100235910854 n^{6}+743507406440902968826099565735373464311912300715198953756 n^{5}+10482185198234358034203542323078793358086704747948125235370 n^{4}-358887368941302998422547759266156783380721164465922441100717 n^{3}-16692132197347904303847079077614128621693092738860066666955664 n^{2}-253607065151265520306086773033827692794378400667888187767585716 n -1402504220527511122648890591216841569268754477329795326418428720\right) a \! \left(n +26\right)}{21125691349662872656250000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(845739624056196523922573995078240129693595670722370197 n^{7}+151301883049962969795196063941718539402814057382594396627 n^{6}+11570560984145132181393254748789823504852862484633309636407 n^{5}+489324421521579522893415620145517410829971255610216919115545 n^{4}+12323974360772948251811787472304454077837119695534220152530828 n^{3}+184087561797876179007301380032631477161677167243000514322449628 n^{2}+1500831439964568315170147874806419964441163305821597708111879968 n +5102532382189844299279467834558003021688756003948012256949918720\right) a \! \left(n +27\right)}{42251382699325745312500000 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{935909195776 \left(n +5\right) \left(n +4\right) \left(n +3\right) \left(n +2\right) \left(n +1\right) \left(4448877025373106978003637 n^{2}+33290509726602579062344120 n +39825156665327112703345380\right) a \! \left(n +1\right)}{188622244193418505859375 \left(2 n +231\right) \left(n +117\right) \left(n +116\right) \left(n +115\right) \left(n +114\right) \left(n +113\right) \left(2 n +233\right)}-\frac{\left(148921223715785485 n^{2}+33970968144302475826 n +1937360085195761178477\right) a \! \left(n +115\right)}{3941819960286950 \left(n +117\right) \left(2 n +233\right)}, \quad n \geq 116\)

This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 47 rules.

Found on January 25, 2022.

Finding the specification took 4393 seconds.

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