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%I #8 Aug 29 2018 17:55:21
%S 1,1,5,9,28,48,130,226,532,941,2021,3545,7210,12509,24209,41715,77742,
%T 132404,239655,403731,712426,1188079,2052070,3386854,5745200,9388740,
%U 15672560,25376167,41765597,67021171,108932532,173327693,278533669,439653317,699265665
%N Expansion of Product_{k>=1} (1/(1 - x^k))^(sigma_0(k)^2).
%H Vaclav Kotesovec, <a href="/A301747/b301747.txt">Table of n, a(n) for n = 0..10000</a>
%F log(a(n)) ~ sqrt(n) * log(n)^(3/2) / (2*sqrt(3)). - _Vaclav Kotesovec_, Aug 28 2018
%t nmax = 50; CoefficientList[Series[Product[1/(1-x^k)^(DivisorSigma[0, k]^2), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 50; s = 1 - x; Do[s *= Sum[Binomial[DivisorSigma[0, k]^2, j]*(-1)^j*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]]; , {k, 2, nmax}]; CoefficientList[Series[1/s, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 29 2018 *)
%Y Cf. A000005, A006171, A035116, A301746.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 26 2018
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