A303396 Expansion of Product_{k>=1} ((1 - 8*x^k)/(1 + 8*x^k))^(1/8).

1, -2, 0, -42, 86, -1638, 4116, -76662, 218592, -3879766, 11965072, -205722702, 672706566, -11257625386, 38520382716, -630071416794, 2236375718918, -35864826630822, 131232962248816, -2068477295105214, 7767014381299026, -120556991420552658

Offset: 0

Author

Seiichi Manyama, Apr 23 2018

Keywords

• sign

Links

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

Crossrefs

Expansion of Product_{k>=1} ((1 - 2^b*x^k)/(1 + 2^b*x^k))^(1/(2^b)): A002448 (b=0), A303345 (b=1), A303387 (b=2), this sequence (b=3).

Cf. A303382.

Programs

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-8*x^k)/(1+8*x^k))^(1/8)))

Formula

a(n) ~ c * (-8)^n / n^(7/8), where c = (QPochhammer[-1, -1/8] / QPochhammer[-1/8])^(1/8) / Gamma(1/8) = 0.14075750048358669653215841485... - Vaclav Kotesovec, Apr 25 2018