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A303353 Expansion of Product_{n>=1} 1/(1 + 9*x^n)^(1/3). 2
1, -3, 15, -120, 915, -7086, 56661, -462405, 3819165, -31843110, 267610443, -2263491255, 19246265025, -164379723735, 1409306287470, -12122528944620, 104575462390842, -904411297029585, 7839310835762475, -68086561401745275, 592417977205534017 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

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

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 *)

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.

Sequence in context: A068859 A006454 A225115 * A112228 A260511 A093571

Adjacent sequences:  A303350 A303351 A303352 * A303354 A303355 A303356

KEYWORD

sign

AUTHOR

Seiichi Manyama, Apr 22 2018

STATUS

approved

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Last modified October 16 06:08 EDT 2019. Contains 328046 sequences. (Running on oeis4.)