A307521 Expansion of Product_{k>=1} ((1 + x)^k + x^k)/((1 + x)^k - x^k).

1, 2, 2, 2, 0, 2, -2, 2, 0, -4, 8, -4, -26, 112, -288, 560, -832, 782, 274, -3378, 9424, -17498, 21182, -2154, -78180, 284594, -700018, 1381802, -2250316, 2877674, -2172870, -1955998, 12715122, -33812990, 67322842, -108956110, 139447006, -110023870, -83188990, 651268018

Offset: 0

Author

Seiichi Manyama, Apr 12 2019

Keywords

• sign

Crossrefs

Cf. A002448, A307520, A307522, A318570.

Programs

Mathematica

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 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+x)^k+x^k)/((1+x)^k-x^k)))

Formula

G.f.: 1/theta_4(x/(1 + x)), where theta_4() is the Jacobi theta function.