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%I #13 May 14 2021 02:53:12
%S 1,-2,2,-2,4,-10,22,-42,72,-116,188,-332,662,-1432,3148,-6736,13784,
%T -26894,50254,-90782,160856,-285230,518170,-983710,1964800,-4090002,
%U 8705322,-18582722,39219572,-81148034,163946630,-323136562,622125982,-1173528562,2179230066
%N Expansion of Product_{k>=1} ((1 + x)^k - x^k)/((1 + x)^k + x^k).
%F G.f.: theta_4(x/(1 + x)), where theta_4() is the Jacobi theta function.
%t m = 34; 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, A307521, A318570.
%K sign
%O 0,2
%A _Seiichi Manyama_, Apr 12 2019
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