A303490 Expansion of Product_{k>=1} ((1 - 4^k*x^k)/(1 + 4^k*x^k))^(1/4^k).

1, -2, 0, -10, 22, -102, 84, -950, 3360, -18006, 21968, -162126, 613830, -2772010, 3847740, -38669210, 145735622, -567469350, 901506480, -6688787966, 27166965906, -137118406226, 234942672620, -1425038557410, 6527750118052, -27227710098826

Offset: 0

Author

Seiichi Manyama, Apr 24 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A303394, A303439, A303442, A303491.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Exp[Sum[(1 - (-1)^j) / (j*(1 - 1/(4^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-4^k*x^k)/(1+4^k*x^k))^(1/4^k)))

Formula

G.f.: exp(Sum_{j>=1} ((1 - (-1)^j) / (j*(1 - 1/(4^(j-1)*x^j))) )). - Vaclav Kotesovec, Apr 25 2018