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%I #13 Sep 08 2022 08:44:46
%S 1,8,44,208,854,3200,11176,36752,115089,345600,1000484,2804544,
%T 7639718,20280672,52593032,133509840,332340788,812455304,1953140484,
%U 4622589504,10782030284,24807035200,56345836888,126438750160,280490520517,615512622608,1336825948592,2875079590304
%N Expansion of Product_{m>=1} (1 + m*q^m)^8.
%H G. C. Greubel, <a href="/A022636/b022636.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp(8*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)^8, {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)^8)) \\ _G. C. Greubel_, Feb 17 2018
%o (Magma) Coefficients(&*[(1+m*x^m)^8:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 17 2018
%Y Column k=8 of A297321.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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