A307520 Expansion of Product_{k>=1} ((1 - x)^k - x^k)/((1 - x)^k + x^k).

1, -2, -2, -2, 0, 6, 18, 38, 68, 108, 148, 148, -2, -552, -2004, -5280, -11960, -24590, -46990, -84254, -141476, -218654, -295794, -295374, 3540, 1148110, 4378918, 12332318, 30327568, 68633710, 146303026, 297349758, 580052778, 1089382158, 1969425038, 3413378318, 5614375970

Offset

0,2

Links

Table of n, a(n) for n=0..36.

Formula

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

Mathematica

m = 36; 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

Convolution inverse of A318570.

Cf. A002448, A307521, A307522.

Sequence in context: A136663 A165490 A298819 * A265648 A181230 A262372

Adjacent sequences: A307517 A307518 A307519 * A307521 A307522 A307523

Keyword

sign

Author

Seiichi Manyama, Apr 12 2019

Status

approved