A318174 Expansion of Hypergeometric function F(5/12, 13/12; 2; 1728*x) in powers of x.

1, 390, 331500, 355699500, 428760177300, 554472661284360, 751706507941225200, 1054268377387568343000, 1516916483664479584186500, 2226631142488300765641223800, 3321243012135549422030449420080, 5019605916068500831023292873530000, 7670343963284674539098285610205650000

Offset

0,2

Comments

A145492 is the convolution of A092870 and this sequence.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..310

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) = (12^n/(n!*(n+1)!)) * Product_{k=0..n-1} (12k+5)*(12k+13).

a(n) = (12*n+1)*A092870(n)/(n+1).

a(n) ~ 12^(3*n + 1) / (Gamma(1/12) * Gamma(5/12) * n^(3/2)). - Vaclav Kotesovec, Aug 21 2018

Prog

(PARI) {a(n) = 12^n/(n!*(n+1)!)*prod(k=0, n-1, (12*k+5)*(12*k+13))}

Crossrefs

F([b/2]+5/12, [(b+1)/2]+1/12; b+1; 1728*x): A092870 (b=0), this sequence (b=1), A318200 (b=2), A318201 (b=3).

Cf. A145492.

Sequence in context: A236612 A332419 A207575 * A158004 A264448 A160184

Adjacent sequences: A318171 A318172 A318173 * A318175 A318176 A318177

Keyword

nonn

Author

Seiichi Manyama, Aug 20 2018

Status

approved