A296043 a(n) = [x^n] Product_{k>=1} ((1 + x^(2*k-1))/(1 + x^(2*k)))^n.

1, 1, -1, -5, -1, 31, 65, -90, -641, -644, 3329, 11386, -1471, -87021, -164634, 317935, 1881471, 1418719, -11370760, -33937951, 17468929, 294971868, 468897758, -1304743033, -6275603903, -2804572819, 42665919997, 109181454826, -106020803386, -1063546684834, -1362993953395

Offset: 0

Author

Ilya Gutkovskiy, Dec 03 2017

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Main diagonal of A296067.

Cf. A029838, A029839, A029840, A029841, A029842, A029843, A029844, A029845, A296044, A296045.

Programs

Mathematica

Table[SeriesCoefficient[Product[((1 + x^(2 k - 1))/(1 + x^(2 k)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[(x^(1/8) EllipticTheta[2, 0, x^(1/2)]/EllipticTheta[2, 0, x])^n, {x, 0, n}], {n, 0, 30}]