A289557 Expansion of Hypergeometric function F(1/12, 7/12; 1; 1728*x) in powers of x.

1, 84, 62244, 64318800, 76748408100, 99281740718160, 135254824771706640, 191023977418391557440, 277044462249611005649700, 410066847753461267769800400, 616822552390756438979333761680, 940037569843512813004504652800320

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..309

R. S. Maier, Nonlinear differential equations satisfied by certain classical modular forms, arXiv:0807.1081 [math.NT], 2008-2010, p. 34 equation (7.30).

Formula

a(n) * n^2 = a(n-1) * 12 * (12*n - 5) * (12*n - 11).

a(n) = (12^n/n!^2) * Product_{k=0..n-1} (12k+1)*(12k+7).

a(n) ~ 2^(6*n-5/6) * 3^(3*n) / (sqrt(Pi) * Gamma(1/6) * n^(4/3)). - Vaclav Kotesovec, Jul 08 2017

Prog

(PARI) a(n) = (12^n/n!^2) * prod(k=0, n-1, (12*k+1)*(12*k+7)); \\ Michel Marcus, Jul 08 2017

Crossrefs

Cf. A092870, A289325.

Sequence in context: A184896 A203093 A290274 * A202580 A292196 A076230

Adjacent sequences: A289554 A289555 A289556 * A289558 A289559 A289560

Keyword

nonn

Author

Seiichi Manyama, Jul 07 2017

Status

approved