A303397 Expansion of Product_{k>=1} (1 - 2*x^k)/(1 + 2*x^k).

1, -4, 4, -4, 20, -36, 52, -116, 244, -500, 964, -1876, 3876, -7780, 15332, -30628, 61684, -123460, 246036, -491988, 985492, -1971284, 3939556, -7878068, 15762692, -31527428, 63041220, -126078916, 252185044, -504375460, 1008698036, -2017385268, 4034873268

Offset: 0

Author

Seiichi Manyama, Apr 23 2018

Keywords

• sign

Crossrefs

Expansion of Product_{k>=1} (1 - b*x^k)/(1 + b*x^k): A002448 (b=1), this sequence (b=2), A303398 (b=3).

Cf. A261584, A303345.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 - 2*x^k)/(1 + 2*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-2*x^k)/(1+2*x^k)))

Formula

a(n) ~ c * (-2)^n, where c = QPochhammer[-1, -1/2]/QPochhammer[-1/2] = 0.93943604828296530723602398257349307281... - Vaclav Kotesovec, Apr 25 2018