A303353 Expansion of Product_{n>=1} 1/(1 + 9*x^n)^(1/3).

1, -3, 15, -120, 915, -7086, 56661, -462405, 3819165, -31843110, 267610443, -2263491255, 19246265025, -164379723735, 1409306287470, -12122528944620, 104575462390842, -904411297029585, 7839310835762475, -68086561401745275, 592417977205534017

Offset: 0

Author

Seiichi Manyama, Apr 22 2018

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 1/3, g(n) = -9.

Links

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

Crossrefs

Expansion of Product_{n>=1} 1/(1 + b^2*x^n)^(1/b): A081362 (b=1), A303352 (b=2), this sequence (b=3).

Cf. A303349.

Programs

Maple

seq(coeff(series(mul(1/(1+9*x^k)^(1/3), k = 1..n), x, n+1), x, n), n = 0..25); # Muniru A Asiru, Apr 22 2018

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1 + 9*x^k)^(1/3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)

Formula

a(n) ~ c * (-9)^n / n^(2/3), where c = 1 / (Gamma(1/3) * QPochhammer[-1/9]^(1/3)) = 0.361746646328749408912877789757526727... - Vaclav Kotesovec, Apr 25 2018