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%I #8 Apr 19 2017 10:16:19
%S 1,1,4,7,18,32,72,127,257,454,861,1497,2719,4654,8171,13781,23564,
%T 39159,65559,107455,176712,286000,463200,740910,1184123,1873656,
%U 2959376,4636145,7245680,11246590,17409731,26792371,41114202,62769820,95553779,144803917
%N Expansion of Product_{k>=1} ((1 + x^(2*k)) / (1 - x^k))^k.
%H Vaclav Kotesovec, <a href="/A285462/b285462.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(1/12 + 3 * (19*Zeta(3))^(1/3) * n^(2/3) / 4) * (19*Zeta(3))^(7/36) / (A * 2^(7/6) * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.
%t nmax = 40; CoefficientList[Series[Product[((1+x^(2*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A156616, A285447, A285460, A285461.
%Y Cf. A279328.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 19 2017