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%I #23 May 14 2021 08:36:43
%S 1,1,-4,5,3,-17,33,-61,67,63,-392,803,-1070,898,482,-4449,11362,
%T -18630,21105,-11067,-24871,103562,-227004,359040,-417697,266106,
%U 312987,-1578543,3635615,-6157911,8155892,-7689028,1502546,14707881,-44539735,87849728,-136927058,171008704
%N Expansion of Product_{k>=1} 1/(1+x^k)^((-1)^k*k^2).
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = (-1)^n * n^2, g(n) = -1.
%H Seiichi Manyama, <a href="/A307484/b307484.txt">Table of n, a(n) for n = 0..10000</a>
%t m = 37; CoefficientList[Series[Product[1/(1+x^k)^((-1)^k*k^2), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 14 2021 *)
%t nmax = 40; CoefficientList[Series[Product[(1 + x^(2*k - 1))^((2*k - 1)^2)/(1 + x^(2*k))^(4*k^2), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 14 2021 *)
%o (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+x^k)^((-1)^k*k^2)))
%Y Product_{k>=1} 1/(1+x^k)^((-1)^k*k^b): A029838 (b=0), A284467 (b=1), this sequence (b=2).
%Y Cf. A177155, A307462.
%K sign
%O 0,3
%A _Seiichi Manyama_, Apr 10 2019
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