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A318201
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Expansion of Hypergeometric function F(17/12, 25/12; 4; 1728*x) in powers of x.
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3
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1, 1275, 1641690, 2198770140, 3046553083980, 4336768315045530, 6307588582660665300, 9334870668704489748840, 14013762435241053769769940, 21290019308561214243784932180, 32671991169676632627962261307000, 50573696461217634323724960067290000, 78871365421150941315659866056940998000
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OFFSET
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0,2
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COMMENTS
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A145494 is the convolution of A092870 and this sequence.
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..309
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998
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FORMULA
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a(n) = (6*12^n/(n!*(n+3)!)) * Product_{k=0..n-1} (12k+17)*(12k+25).
a(n) = 6*(12*n+1)*(12*n+5)*(12*n+13)*A092870(n)/(65*(n+1)*(n+2)*(n+3)).
a(n) ~ 2^(6*n + 7) * 3^(3*n + 4) / (65 * Gamma(1/12) * Gamma(5/12) * n^(3/2)). - Vaclav Kotesovec, Aug 21 2018
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PROG
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(PARI) {a(n) = 6*12^n/(n!*(n+3)!)*prod(k=0, n-1, (12*k+17)*(12*k+25))}
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CROSSREFS
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F([b/2]+5/12, [(b+1)/2]+1/12; b+1; 1728*x): A092870 (b=0), A318174 (b=1), A318200 (b=2), this sequence (b=3).
Cf. A145494.
Sequence in context: A187465 A325604 A230758 * A236013 A282440 A211685
Adjacent sequences: A318198 A318199 A318200 * A318202 A318203 A318204
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Aug 21 2018
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STATUS
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approved
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