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Generating function in Maple format
Minimal polynomial in Maple format
First 15 coefficients

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Av(1234, 1243) Av(1234, 1324) Av(1234, 1342) Av(1234, 1432) Av(1234, 2143) Av(1234, 2341) Av(1234, 2413) Av(1234, 2431) Av(1234, 3412) Av(1234, 3421) Av(1234, 4231) Av(1234, 4321) Av(1243, 1324) Av(1243, 1342) Av(1243, 1432) Av(1243, 2134) Av(1243, 2143) Av(1243, 2314) Av(1243, 2341) Av(1243, 2413) Av(1243, 2431) Av(1243, 3214) Av(1243, 3241) Av(1243, 3412) Av(1243, 3421)