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%I #29 Sep 08 2022 08:44:46
%S 1,3,9,28,69,174,413,933,2046,4391,9168,18675,37522,73725,142893,
%T 273159,514512,957666,1762837,3208884,5783727,10330732,18280590,
%U 32086827,55880614,96579240,165733335,282513246,478419366,805196022,1347288750,2241377166,3708721887
%N Expansion of Product_{m>=1} (1 + m*q^m)^3.
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -3, g(n) = -n. - _Seiichi Manyama_, Dec 29 2017
%H Seiichi Manyama, <a href="/A022631/b022631.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp(3*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 08 2018
%t With[{nmax=34}, CoefficientList[Series[Product[(1+k*q^k)^3, {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)^3)) \\ _G. C. Greubel_, Feb 16 2018
%o (Magma) Coefficients(&*[(1+m*x^m)^3:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 16 2018
%Y Column k=3 of A297321.
%K nonn
%O 0,2
%A _N. J. A. Sloane_