A303382 Expansion of Product_{n>=1} ((1 + 8*x^n)/(1 - 8*x^n))^(1/8).

1, 2, 4, 50, 98, 1830, 4576, 83950, 236500, 4211766, 12903260, 222377926, 723722602, 12136867530, 41382435824, 678060771778, 2400028798290, 38546050682278, 140724756748476, 2220907298526934, 8323586858891766, 129340015891714962, 495838256186203600

Offset: 0

Author

Seiichi Manyama, Apr 22 2018

Keywords

• nonn

Links

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

Crossrefs

Expansion of Product_{n>=1} ((1 + 2^b*x^n)/(1 - 2^b*x^n))^(1/(2^b)): A015128 (b=0), A303346 (b=1), A303360 (b=2), this sequence (b=3).

Cf. A303381.

Programs

Maple

seq(coeff(series(mul(((1+8*x^k)/(1-8*x^k))^(1/8), k = 1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 23 2018

Mathematica

nmax = 25; CoefficientList[Series[Product[((1 + 8*x^k)/(1 - 8*x^k))^(1/8), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 23 2018 *)
nmax = 30; CoefficientList[Series[(-7*QPochhammer[-8, x] / (9*QPochhammer[8, x]))^(1/8), {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 23 2018 *)

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) = 0.15003359366795844474467456149... - Vaclav Kotesovec, Apr 23 2018