A303130 Expansion of Product_{n>=1} (1 + (9*x)^n)^(-1/3).

1, -3, -9, -288, 459, -19278, -1539, -1265301, 10734525, -147277926, 520204923, -7511358663, 88687160577, -668191863951, 5357547144702, -87542760890124, 967961569696722, -5115624735401361, 46065749188891275, -430898393089547667, 6203508335817169257

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) = 1/3, g(n) = -9^n.

Links

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

Crossrefs

Expansion of Product_{n>=1} (1 + ((b^2)*x)^n)^(-1/b): A081362 (b=1), A298993 (b=2), this sequence (b=3), A303131 (b=4), A303132 (b=5).

Cf. A303074.

Programs

Mathematica

CoefficientList[Series[(2/QPochhammer[-1, 9*x])^(1/3), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 20 2018 *)

PARI

N=99; x='x+O('x^N); Vec(prod(k=1, N, (1 + (9*x)^k)^(-1/3))) \\ Altug Alkan, Apr 20 2018

Formula

a(n) ~ (-1)^n * exp(Pi*sqrt(n/18)) * 3^(2*n - 1/2) / (2^(7/4) * n^(3/4)). - Vaclav Kotesovec, Apr 20 2018