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Expansion of Product_{m>=1} 1/(1 - m*q^m)^8.
2

%I #12 Sep 08 2022 08:44:46

%S 1,8,52,272,1274,5408,21448,80080,285043,972496,3200644,10199456,

%T 31592350,95366176,281269560,812094448,2299480441,6394796832,

%U 17489643664,47096042032,124993380566,327249781952

%N Expansion of Product_{m>=1} 1/(1 - m*q^m)^8.

%H G. C. Greubel, <a href="/A022732/b022732.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(8*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018

%t With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-8, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Jul 25 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-8)) \\ _G. C. Greubel_, Jul 25 2018

%o (Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^8:m in [1..n]])); // _G. C. Greubel_, Jul 25 2018

%Y Column k=8 of A297328.

%K nonn

%O 0,2

%A _N. J. A. Sloane_