A318200 Expansion of Hypergeometric function F(17/12, 13/12; 3; 1728*x) in powers of x.

1, 884, 961350, 1166694360, 1514952626460, 2059469884770480, 2894070055573717020, 4170217137221937001200, 6128342594004497520113460, 9149429785497381327907574160, 13838512550564789258460205917000, 21159569553888757349236649959188000, 32653750015126185895018415883446910000

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