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%I #34 Sep 08 2022 08:44:46
%S 1,-2,-1,-2,9,-2,10,-16,38,-98,53,-116,340,-434,463,-990,2378,-2792,
%T 3660,-7058,11454,-18900,24104,-36206,81623,-119400,128194,-248062,
%U 447066,-576154,880401,-1415926,2297516,-3724290,4854450,-7299306,13411402,-19129752,25135890,-42841396,71321016
%N Expansion of Product_{m>=1} (1 + m*q^m)^-2.
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 2, g(n) = -n. - _Seiichi Manyama_, Dec 30 2017
%H Seiichi Manyama, <a href="/A022694/b022694.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: exp(-2*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 08 2018
%t With[{nmax=50}, CoefficientList[Series[Product[1/(1+k*q^k)^2, {k,1,nmax}], {q, 0, nmax}],q]] (* _G. C. Greubel_, Feb 22 2018 *)
%o (PARI) apply(x->round(x), Vec(prodinf(m=1, 1/(1+m*q^m)^2+O(q^50)))) \\ _Michel Marcus_, Dec 30 2017
%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,1/(1+n*q^n)^2)) \\ _G. C. Greubel_, Feb 25 2018
%o (Magma) Coefficients(&*[1/(1+m*x^m)^2:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 25 2018
%Y Column k=2 of A297325.
%K sign
%O 0,2
%A _N. J. A. Sloane_
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