A303131 Expansion of Product_{n>=1} (1 + (16*x)^n)^(-1/4).

1, -4, -24, -1248, 1632, -267136, -669440, -56925184, 597165568, -19934894080, 61831327744, -3209599664128, 47593545383936, -840449808072704, 8113679782510592, -350055154021040128, 5703847053344768000, -57129722970675609600, 704939718429511778304

Offset: 0

Author

Seiichi Manyama, Apr 19 2018

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/4, g(n) = -16^n.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Expansion of Product_{n>=1} (1 + ((b^2)*x)^n)^(-1/b): A081362 (b=1), A298993 (b=2), A303130 (b=3), this sequence (b=4), A303132 (b=5).

Cf. A303124, A303135.

Programs

Mathematica

CoefficientList[Series[(2/QPochhammer[-1, 16*x])^(1/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 20 2018 *)

Formula

a(n) ~ (-1)^n * exp(Pi*sqrt(n/24)) * 2^(4*n - 9/4) / (3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 20 2018