%I #5 Oct 15 2015 13:08:10
%S 1,1,3,5,12,21,40,71,130,221,387,648,1095,1800,2964,4792,7730,12301,
%T 19510,30619,47859,74179,114469,175427,267684,406039,613325,921671,
%U 1379500,2055313,3050652,4509385,6641966,9746452,14254242,20775255,30184451,43715711
%N Expansion of Product_{k>=1} ((1 - x^(3*k))/(1 - x^k))^k.
%H Vaclav Kotesovec, <a href="/A263346/b263346.txt">Table of n, a(n) for n = 0..1000</a>
%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) ~ 2^(1/6) * Zeta(3)^(1/6) * exp(6^(1/3) * Zeta(3)^(1/3) * n^(2/3)) / (3^(11/12) * sqrt(Pi) * n^(2/3)).
%t nmax=40; CoefficientList[Series[Product[((1 - x^(3*k))/(1 - x^k))^k,{k,1,nmax}],{x,0,nmax}],x]
%Y Cf. A000726, A000219, A262876, A262877, A262878, A262879, A263345.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 15 2015