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Expansion of Product_{k>=1} ((1 + x^(4*k)) / (1 - x^k))^k.
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%I #8 Apr 19 2017 11:51:28

%S 1,1,3,6,14,25,51,92,175,308,554,957,1670,2820,4778,7940,13169,21511,

%T 35032,56405,90453,143716,227342,356950,557977,866588,1340109,2060912,

%U 3156274,4810016,7301490,11034661,16614681,24916208,37234864,55440054,82274277

%N Expansion of Product_{k>=1} ((1 + x^(4*k)) / (1 - x^k))^k.

%H Vaclav Kotesovec, <a href="/A285460/b285460.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ exp(1/12 + 3 * 2^(-8/3) * (67*Zeta(3))^(1/3) * n^(2/3)) * (67*Zeta(3))^(7/36) / (A * 2^(14/9) * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.

%t nmax = 40; CoefficientList[Series[Product[((1+x^(4*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A156616, A285462, A285447, A285461, A285472.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Apr 19 2017