A303353 -id:A303353 - cp's OEIS frontend

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

Seiichi Manyama, Apr 22 2018

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

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

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.

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

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

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

cp's OEIS Frontend

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

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