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A318200 Expansion of Hypergeometric function F(17/12, 13/12; 3; 1728*x) in powers of x. 3
1, 884, 961350, 1166694360, 1514952626460, 2059469884770480, 2894070055573717020, 4170217137221937001200, 6128342594004497520113460, 9149429785497381327907574160, 13838512550564789258460205917000, 21159569553888757349236649959188000, 32653750015126185895018415883446910000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A145493 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) = (2*12^n/(n!*(n+2)!)) * Product_{k=0..n-1} (12k+17)*(12k+13).

a(n) = 2*(12*n+1)*(12*n+5)*A092870(n)/(5*(n+1)*(n+2)).

a(n) ~ 2^(6*n + 5) * 3^(3*n + 2) / (5 * Gamma(1/12) * Gamma(5/12) * n^(3/2)). - Vaclav Kotesovec, Aug 21 2018

PROG

(PARI) {a(n) = 2*12^n/(n!*(n+2)!)*prod(k=0, n-1, (12*k+17)*(12*k+13))}

CROSSREFS

F([b/2]+5/12, [(b+1)/2]+1/12; b+1; 1728*x): A092870 (b=0), A318174 (b=1), this sequence (b=2), A318201 (b=3).

Cf. A145493.

Sequence in context: A207131 A253507 A282156 * A295443 A261760 A031794

Adjacent sequences:  A318197 A318198 A318199 * A318201 A318202 A318203

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 21 2018

STATUS

approved

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Last modified December 5 08:36 EST 2021. Contains 349543 sequences. (Running on oeis4.)