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%I #13 May 14 2021 02:56:09
%S 1,2,2,2,0,2,-2,2,0,-4,8,-4,-26,112,-288,560,-832,782,274,-3378,9424,
%T -17498,21182,-2154,-78180,284594,-700018,1381802,-2250316,2877674,
%U -2172870,-1955998,12715122,-33812990,67322842,-108956110,139447006,-110023870,-83188990,651268018
%N Expansion of Product_{k>=1} ((1 + x)^k + x^k)/((1 + x)^k - x^k).
%F G.f.: 1/theta_4(x/(1 + x)), where theta_4() is the Jacobi theta function.
%t m = 39; CoefficientList[Series[Product[((1 + x)^k + x^k)/((1 + x)^k - x^k), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 14 2021 *)
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+x)^k+x^k)/((1+x)^k-x^k)))
%Y Cf. A002448, A307520, A307522, A318570.
%K sign
%O 0,2
%A _Seiichi Manyama_, Apr 12 2019