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%I #24 May 30 2018 15:12:54
%S 1,3,9,28,72,183,443,1026,2313,5072,10860,22767,46862,94806,188886,
%T 371068,719493,1378449,2611540,4896291,9090651,16723930,30501744,
%U 55177932,99048719,176500572,312330813,549033172
%N Expansion of Product_{m>=1} (1 + q^m)^(3*m).
%H Seiichi Manyama, <a href="/A027346/b027346.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from G. C. Greubel)
%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, p. 19.
%F a(n) ~ exp(2^(-4/3) * 3^(5/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(11/12) * 3^(1/6) * sqrt(Pi) * n^(2/3)). - _Vaclav Kotesovec_, Aug 17 2015
%F G.f.: exp(3*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, May 30 2018
%t nmax = 40; CoefficientList[Series[Product[(1+x^k)^(3*k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 17 2015 *)
%Y Column k=3 of A277938.
%Y Cf. A026007, A026011, A027906.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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