%I #7 Apr 19 2017 09:42:06

%S 1,1,3,7,14,27,56,101,190,347,617,1082,1895,3230,5490,9226,15332,

%T 25259,41356,67021,107989,172789,274613,433815,681650,1064661,1654739,

%U 2559029,3938438,6033967,9205152,13982675,21156174,31886290,47879210,71636483,106814323

%N Expansion of Product_{k>=1} ((1 + x^(3*k)) / (1 - x^k))^k.

%H Vaclav Kotesovec, <a href="/A285447/b285447.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ exp(1/12 + 2^(-4/3) * 3^(2/3) * (13*Zeta(3))^(1/3) * n^(2/3)) * (13*Zeta(3))^(7/36) / (A * 2^(7/9) * 3^(25/36) * sqrt(Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.

%t nmax = 40; CoefficientList[Series[Product[((1+x^(3*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A266648, A285446.

%Y Cf. A156616, A285462, A285460, A285461.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Apr 19 2017