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%I #19 Sep 08 2022 08:44:46
%S 1,-2,-3,2,4,16,-3,6,-31,-72,-15,-44,9,154,521,48,426,66,2,-1618,
%T -3782,-210,-3882,-1282,1119,3940,10867,37208,11647,20574,6256,534,
%U -1915,-120006,-161755,-312622,-93923,-271850,-25782,-197026,1112303,574604,209604,3038822,4187500,1398330
%N Expansion of Product_{m>=1} (1 - m*q^m)^2.
%H Vaclav Kotesovec, <a href="/A022662/b022662.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: exp(-2*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018
%t nmax = 50; poly = ConstantArray[0, nmax+1]; poly[[1]] = 1; poly[[2]] = -2; poly[[3]] = 1; Do[Do[Do[poly[[j+1]] -= k*poly[[j-k+1]], {j, nmax, k, -1}];, {p, 1, 2}], {k, 2, nmax}]; poly (* _Vaclav Kotesovec_, Jan 07 2016 *)
%t With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^2, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Feb 18 2018 *)
%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^2)) \\ _G. C. Greubel_, Feb 18 2018
%o (Magma) Coefficients(&*[(1-m*x^m)^2:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 18 2018
%Y Cf. A022662, A022726.
%Y Column k=2 of A297323.
%K sign
%O 0,2
%A _N. J. A. Sloane_