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%I #9 Aug 28 2018 13:00:48
%S 1,1,6,18,52,142,404,1018,2624,6645,16124,38857,92245,214841,494098,
%T 1125062,2522188,5604930,12327860,26838595,57913194,123951482,
%U 263019720,553989989,1158449522,2405179547,4961047246,10168544537,20714279168,41952595411,84494479578
%N Expansion of Product_{k>=1} (1 + k*x^k)^sigma(k), where sigma = A000203.
%H Vaclav Kotesovec, <a href="/A318484/b318484.txt">Table of n, a(n) for n = 0..10000</a>
%t nmax = 40; CoefficientList[Series[Product[(1+k*x^k)^DivisorSigma[1, k], {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 40; s = 1 + x; Do[s *= Sum[Binomial[DivisorSigma[1, k], j]*k^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[s, x]
%Y Cf. A000203, A022629, A266891, A318416, A107742, A192065, A318483.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Aug 27 2018