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%I #13 Sep 08 2022 08:44:46
%S 1,5,20,75,240,726,2075,5620,14645,36875,90057,214065,497170,1129670,
%T 2517425,5512125,11871310,25184930,52686885,108786970,221894842,
%U 447455885,892609420,1762608545,3447282925,6680871925,12835968690,24459374345,46243132855,86773966825,161664667295
%N Expansion of Product_{m>=1} (1 + m*q^m)^5.
%H G. C. Greubel, <a href="/A022633/b022633.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp(5*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 08 2018
%t With[{nmax=50}, CoefficientList[Series[Product[(1+k*q^k)^5, {k,1,nmax}], {q, 0, nmax}],q]] (* _G. C. Greubel_, Feb 16 2018 *)
%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^5)) \\ _G. C. Greubel_, Feb 16 2018
%o (Magma) Coefficients(&*[(1+m*x^m)^5:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 16 2018
%Y Column k=5 of A297321.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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