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A318174 Expansion of Hypergeometric function F(5/12, 13/12; 2; 1728*x) in powers of x. 4
1, 390, 331500, 355699500, 428760177300, 554472661284360, 751706507941225200, 1054268377387568343000, 1516916483664479584186500, 2226631142488300765641223800, 3321243012135549422030449420080, 5019605916068500831023292873530000, 7670343963284674539098285610205650000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 25 23:28 EDT 2020. Contains 334607 sequences. (Running on oeis4.)