A303345 Expansion of Product_{k>=1} ((1 - 2*x^k)/(1 + 2*x^k))^(1/2).

1, -2, 0, -2, 6, -6, 12, -22, 48, -94, 160, -318, 622, -1210, 2268, -4482, 8678, -16998, 32632, -64366, 124674, -245866, 476108, -940866, 1829148, -3617066, 7040112, -13937530, 27186810, -53857062, 105196572, -208546726, 407944704, -809175966, 1584713040

Offset: 0

Author

Seiichi Manyama, Apr 22 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A303306, A303346, A303439.

Expansion of Product_{k>=1} ((1 - 2^b*x^k)/(1 + 2^b*x^k))^(1/(2^b)): A002448 (b=0), this sequence (b=1), A303387 (b=2), A303396 (b=3).

Programs

Maple

seq(coeff(series(mul(((1-2*x^k)/(1+2*x^k))^(1/2), k = 1..n), x, n+1), x, n), n=0..40); # Muniru A Asiru, Apr 22 2018

PARI

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

Formula

a(n) ~ c * (-2)^n / sqrt(Pi*n), where c = (QPochhammer[-1, -1/2] / QPochhammer[-1/2])^(1/2) = 0.96924509195711964009315.... - Vaclav Kotesovec, Apr 25 2018