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A262879 Expansion of Product_{k>=1} (1+x^(3*k-2))^k.

%I A262879 #14 Apr 22 2021 08:29:10
%S A262879 1,1,0,0,2,2,0,3,4,1,4,10,6,5,16,14,9,28,32,17,40,63,41,63,112,83,94,
%T A262879 187,171,156,301,319,260,467,580,465,713,981,818,1095,1627,1452,1682,
%U A262879 2584,2510,2632,4047,4266,4162,6181,7054,6685,9396,11423,10753,14132
%N A262879 Expansion of Product_{k>=1} (1+x^(3*k-2))^k.
%H A262879 Vaclav Kotesovec, <a href="/A262879/b262879.txt">Table of n, a(n) for n = 0..10000</a>
%H A262879 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 A262879 a(n) ~ exp(2^(-4/3) * 3^(2/3) * Zeta(3)^(1/3) * n^(2/3) + Pi^2 * n^(1/3) / (2^(2/3) * 3^(8/3) * Zeta(3)^(1/3)) - Pi^4/(2916*Zeta(3))) * Zeta(3)^(1/6) / (2^(19/36) * 3^(2/3) * sqrt(Pi) * n^(2/3)).
%t A262879 nmax=100; CoefficientList[Series[Product[(1+x^(3k-2))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%t A262879 nmax=100; CoefficientList[Series[E^Sum[(-1)^(j+1)/j*x^j/(1-x^(3j))^2,{j,1,nmax}],{x,0,nmax}],x]
%t A262879 Clear[a]; a[n_]:=a[n] = If[n==0, 1, Sum[Sum[d*{0, 2*Floor[d/6] + 1, -Floor[d/6] - 1, 0, 2*Floor[d/6] + 2, 0}[[1 + Mod[d, 6]]], {d, Divisors[j]}] * a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 100}]
%Y A262879 Cf. A026007, A027346, A035528, A262876, A262877, A262878, A262884, A262949.
%K A262879 nonn
%O A262879 0,5
%A A262879 _Vaclav Kotesovec_, Oct 04 2015