|
%I #18 Apr 15 2017 19:49:00
%S 1,1,3,3,10,15,27,44,79,128,211,331,549,843,1338,2061,3195,4851,7384,
%T 11104,16696,24774,36817,54173,79560,116067,168880,244293,352480,
%U 506012,724531,1032762,1468271,2079525,2937102,4134399,5804795,8124459,11342952,15791650
%N Expansion of Product_{k>=1} 1 / ((1-x^(3*k-1))^(3*k-1) * (1-x^(3*k-2))^(3*k-2)).
%C Convolution of A262946 and A262947.
%H Seiichi Manyama, <a href="/A262923/b262923.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Vaclav Kotesovec)
%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015.
%F a(n) ~ exp(-1/6 + 3^(2/3)*(Zeta(3)/2)^(1/3) * n^(2/3)) * A^2 * Zeta(3)^(1/9) / (2^(5/18) * 3^(31/36) * sqrt(Pi) * n^(11/18)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
%t nmax=60; CoefficientList[Series[Product[1/((1 - x^(3*k-1))^(3*k-1) * (1 - x^(3*k-2))^(3*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A262883, A262876, A262877, A262924, A035386, A035382, A262946, A262947.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 04 2015
|
