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%I #6 May 28 2015 12:52:28
%S 1,0,3,2,11,10,35,40,107,138,310,432,871,1262,2355,3504,6186,9318,
%T 15799,23934,39351,59672,95772,144970,228258,344244,533552,800952,
%U 1225164,1829530,2767227,4109504,6155310,9089834,13497964,19822252,29208812,42660456
%N Expansion of Product_{k>=1} 1/(1-x^k)^(k+(-1)^k).
%H Vaclav Kotesovec, <a href="/A258386/b258386.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ (2*Zeta(3))^(13/36) / (sqrt(3) * Pi * n^(31/36)) * exp(Zeta'(-1) + 3*Zeta(3)^(1/3) * (n/2)^(2/3)), where Zeta(3) = A002117, Zeta'(-1) = A084448 = 1/12 - log(A074962). - _Vaclav Kotesovec_, May 28 2015
%t nmax=40; CoefficientList[Series[Product[1/(1-x^k)^(k+(-1)^k),{k,1,nmax}],{x,0,nmax}],x]
%Y Cf. A000219, A106507.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 28 2015
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