A318201 Expansion of Hypergeometric function F(17/12, 25/12; 4; 1728*x) in powers of x.

1, 1275, 1641690, 2198770140, 3046553083980, 4336768315045530, 6307588582660665300, 9334870668704489748840, 14013762435241053769769940, 21290019308561214243784932180, 32671991169676632627962261307000, 50573696461217634323724960067290000, 78871365421150941315659866056940998000

Offset

0,2

Comments

A145494 is the convolution of A092870 and this sequence.

Links

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

Formula

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

Prog

(PARI) {a(n) = 6*12^n/(n!*(n+3)!)*prod(k=0, n-1, (12*k+17)*(12*k+25))}

Crossrefs

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

Keyword

nonn

Author

Seiichi Manyama, Aug 21 2018

Status

approved