A303352 Expansion of Product_{n>=1} 1/(1 + 4*x^n)^(1/2).

1, -2, 4, -18, 66, -230, 832, -3118, 11764, -44374, 168476, -643974, 2470506, -9503946, 36666736, -141824034, 549717490, -2134650662, 8303024092, -32343942934, 126161860886, -492703658930, 1926278860624, -7538530620746, 29529208903872, -115766389203370

Offset

0,2

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/2, g(n) = -4.

Links

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

Formula

a(n) ~ c * (-4)^n / sqrt(Pi*n), where c = 1 / QPochhammer[-1/4]^(1/2) = 0.91806413264267465793225216525758518... - Vaclav Kotesovec, Apr 25 2018

Maple

seq(coeff(series(mul(1/(1+4*x^k)^(1/2), k = 1..n), x, n+1), x, n), n=0..40); # Muniru A Asiru, Apr 22 2018

Mathematica

nmax = 30; CoefficientList[Series[Product[1/(1 + 4*x^k)^(1/2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)

Crossrefs

Expansion of Product_{n>=1} 1/(1 + b^2*x^n)^(1/b): A081362 (b=1), this sequence (b=2), A303353 (b=3).

Cf. A067855, A303350.

Sequence in context: A241685 A009679 A007727 * A226011 A174085 A325850

Adjacent sequences: A303349 A303350 A303351 * A303353 A303354 A303355

Keyword

sign

Author

Seiichi Manyama, Apr 22 2018

Status

approved