A307522 Expansion of Product_{k>=1} ((1 + x)^k - x^k)/((1 + x)^k + x^k).

1, -2, 2, -2, 4, -10, 22, -42, 72, -116, 188, -332, 662, -1432, 3148, -6736, 13784, -26894, 50254, -90782, 160856, -285230, 518170, -983710, 1964800, -4090002, 8705322, -18582722, 39219572, -81148034, 163946630, -323136562, 622125982, -1173528562, 2179230066

Offset

0,2

Links

Table of n, a(n) for n=0..34.

Formula

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A002448, A307520, A307521, A318570.

Sequence in context: A231382 A360314 A213270 * A130707 A131562 A260786

Adjacent sequences: A307519 A307520 A307521 * A307523 A307524 A307525

Keyword

sign

Author

Seiichi Manyama, Apr 12 2019

Status

approved