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Expansion of Product_{k>=1} (1 + x^k)^(sigma_4(k)).
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%I #12 Oct 26 2018 16:53:13

%S 1,1,17,99,491,2429,12056,56618,259074,1155193,5044288,21585280,

%T 90694483,374661505,1524090522,6111565745,24181962002,94491963120,

%U 364920615165,1393789672170,5268145436728,19715988877445,73096492576283,268589397735778,978533798885874

%N Expansion of Product_{k>=1} (1 + x^k)^(sigma_4(k)).

%H Seiichi Manyama, <a href="/A301548/b301548.txt">Table of n, a(n) for n = 0..3000</a>

%F a(n) ~ exp(6^(2/3) * Pi * (31*Zeta(5)/7)^(1/6) * n^(5/6)/5 + Pi *(7/(31*Zeta(5)))^(1/6) * n^(1/6) / (240*6^(2/3))) * (31*Zeta(5)/7)^(1/12) / (2^(7/6) * 3^(2/3) * n^(7/12)).

%F G.f.: exp(Sum_{k>=1} sigma_5(k)*x^k/(k*(1 - x^(2*k)))). - _Ilya Gutkovskiy_, Oct 26 2018

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

%Y Cf. A001159, A107742, A301542.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 23 2018