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%I #7 Apr 19 2017 09:41:37
%S 1,1,2,6,9,18,36,60,105,191,314,528,896,1447,2355,3831,6071,9619,
%T 15207,23648,36693,56724,86762,132264,200853,302699,454565,680061,
%U 1011540,1499363,2214570,3255796,4770830,6967967,10137577,14703909,21262751,30644816,44041843
%N Expansion of Product_{k>=1} ((1 + x^k) / (1 - x^(3*k)))^k.
%H Vaclav Kotesovec, <a href="/A285446/b285446.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(1/12 + 2^(-4/3) * (93*Zeta(3))^(1/3) * n^(2/3)) * (31*Zeta(3))^(7/36) / (A * 2^(7/9) * 3^(29/36) * sqrt(Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.
%t nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^(3*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A285445, A285447.
%Y Cf. A156616, A000219, A285458, A285459.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 19 2017