%I #13 Sep 08 2022 08:44:46
%S 1,-9,18,51,-171,-117,249,1251,531,-5599,-3006,-2295,20664,50508,
%T -6354,-78597,-292887,-105273,268957,792414,1974312,825753,-2605185,
%U -9778671,-9956433,-4944978,19214991,57418523,78518664,60044976,-124946361,-247193622,-634049649,-623771424,218263050
%N Expansion of Product_{m>=1} (1 - m*q^m)^9.
%H G. C. Greubel, <a href="/A022669/b022669.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp(-9*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)^9, {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)^9)) \\ _G. C. Greubel_, Feb 24 2018
%o (Magma) Coefficients(&*[(1-m*x^m)^9:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 24 2018
%Y Column k=9 of A297323.
%K sign
%O 0,2
%A _N. J. A. Sloane_
%E Terms a(29) onward added by _G. C. Greubel_, Feb 24 2018
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