A303387 Expansion of Product_{k>=1} ((1 - 4*x^k)/(1 + 4*x^k))^(1/4).

1, -2, 0, -10, 22, -102, 244, -1270, 3360, -16886, 46160, -230670, 656550, -3238250, 9474684, -46289530, 138590342, -671116710, 2047182480, -9837322110, 30482926482, -145474988978, 456854466860, -2166890174370, 6884188144964, -32471461699594

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), this sequence (b=2), A303396 (b=3).

Cf. A303360, A303402.

Programs

Maple

seq(coeff(series(mul(((1-4*x^k)/(1+4*x^k))^(1/4), k = 1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 23 2018

PARI

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

Formula

a(n) ~ c * (-4)^n / n^(3/4), where c = (QPochhammer[-1, -1/4] / QPochhammer[-1/4])^(1/4) / Gamma(1/4) = 0.29599817925108933574246285.... - Vaclav Kotesovec, Apr 25 2018