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Expansion of Product_{m>=1} (1 - m*q^m)^7.
2

%I #13 Sep 08 2022 08:44:46

%S 1,-7,7,42,-56,-105,-126,489,987,-651,-833,-6062,-3101,10381,21040,

%T 34720,-20692,-46732,-173642,-238014,25193,614802,1161951,982667,

%U 981253,-3028025,-5721548,-10660692,-7448428,4778767,21412363,79760653,64512273,37376857,-64640856,-220678215

%N Expansion of Product_{m>=1} (1 - m*q^m)^7.

%H G. C. Greubel, <a href="/A022667/b022667.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(-7*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)^7, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Feb 24 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^7)) \\ _G. C. Greubel_, Feb 24 2018

%o (Magma) Coefficients(&*[(1-m*x^m)^7:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 24 2018

%Y Column k=7 of A297323.

%K sign

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(31) onward added by _G. C. Greubel_, Feb 24 2018