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%I #13 Sep 08 2022 08:44:46
%S 1,6,27,110,387,1266,3896,11340,31629,84992,221028,558450,1375615,
%T 3310764,7803069,18044374,40998078,91653990,201842383,438312534,
%U 939439674,1988944070,4162521165,8617025112,17655688602,35823617658,72015578091,143499705550,283544586489,555779906772
%N Expansion of Product_{m>=1} (1 + m*q^m)^6.
%H G. C. Greubel, <a href="/A022634/b022634.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp(6*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)^6, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Feb 17 2018 *)
%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^6)) \\ _G. C. Greubel_, Feb 17 2018
%o (Magma) Coefficients(&*[(1+m*x^m)^6:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 17 2018
%Y Column k=6 of A297321.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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