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Expansion of Product_{m>=1} (1 - m*q^m)^4.
2

%I #25 Sep 08 2022 08:44:46

%S 1,-4,-2,16,9,4,-90,-56,12,60,700,232,-51,-1128,-2006,-3648,-2999,

%T 6292,12004,19192,8829,35024,-43368,-92480,-113859,-227356,-33906,

%U 55072,569221,631620,1193412,1593152,1178350,-2589588,-4131366,-6312376,-12864282,-6891608,-10022026,10270984

%N Expansion of Product_{m>=1} (1 - m*q^m)^4.

%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -4, g(n) = n. - _Seiichi Manyama_, Dec 29 2017

%H Seiichi Manyama, <a href="/A022664/b022664.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(-4*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018

%t With[{nmax=34}, CoefficientList[Series[Product[(1-k*q^k)^4, {k,1,nmax}], {q, 0, nmax}],q]] (* _G. C. Greubel_, Feb 23 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^4)) \\ _G. C. Greubel_, Feb 23 2018

%o (Magma) Coefficients(&*[(1-m*x^m)^4:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 23 2018

%Y Column k=4 of A297323.

%K sign

%O 0,2

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Feb 23 2018