A298993 Expansion of Product_{n>=1} 1/sqrt(1 + (4*x)^n).

1, -2, -2, -36, 54, -476, 556, -6088, 35878, -156844, 444164, -1734648, 11948604, -35313048, 156354328, -864527760, 4733447686, -12692853452, 54065039380, -226098757912, 1278838329812, -5257771138376, 19455009120232, -76455773381360, 453306681446748

Offset: 0

Author

Seiichi Manyama, Jan 31 2018

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000984, A081362, A271235, A298994.

Programs

Mathematica

CoefficientList[Series[Sqrt[2/QPochhammer[-1, 4*x]], {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 18 2018 *)

Formula

a(n) ~ (-1)^n * exp(Pi*sqrt(n/12)) * 4^(n-1) / (3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 18 2018