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%I #20 Jul 08 2017 03:33:35
%S 1,84,62244,64318800,76748408100,99281740718160,135254824771706640,
%T 191023977418391557440,277044462249611005649700,
%U 410066847753461267769800400,616822552390756438979333761680,940037569843512813004504652800320
%N Expansion of Hypergeometric function F(1/12, 7/12; 1; 1728*x) in powers of x.
%H Seiichi Manyama, <a href="/A289557/b289557.txt">Table of n, a(n) for n = 0..309</a>
%H R. S. Maier, <a href="http://arxiv.org/abs/0807.1081">Nonlinear differential equations satisfied by certain classical modular forms</a>, arXiv:0807.1081 [math.NT], 2008-2010, p. 34 equation (7.30).
%F a(n) * n^2 = a(n-1) * 12 * (12*n - 5) * (12*n - 11).
%F a(n) = (12^n/n!^2) * Product_{k=0..n-1} (12k+1)*(12k+7).
%F a(n) ~ 2^(6*n-5/6) * 3^(3*n) / (sqrt(Pi) * Gamma(1/6) * n^(4/3)). - _Vaclav Kotesovec_, Jul 08 2017
%o (PARI) a(n) = (12^n/n!^2) * prod(k=0, n-1, (12*k+1)*(12*k+7)); \\ _Michel Marcus_, Jul 08 2017
%Y Cf. A092870, A289325.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jul 07 2017
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