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A303349 Expansion of Product_{n>=1} 1/(1 - 9*x^n)^(1/3). 3
1, 3, 21, 138, 1029, 7878, 62751, 508521, 4185885, 34819986, 292135143, 2467528563, 20958538377, 178846047741, 1532203949982, 13171424183184, 113562780734352, 981679181808261, 8505577753517235, 73846557073784937, 642328501788394527 (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.

In general, if h > 1 and g.f. = Product_{k>=1} 1/(1 - h^2*x^k)^(1/h), then a(n) ~ h^(2*n) / (Gamma(1/h) * QPochhammer[1/h^2]^(1/h) * n^(1 - 1/h)). - Vaclav Kotesovec, Apr 22 2018

LINKS

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

FORMULA

a(n) ~ c * 3^(2*n) / n^(2/3), where c = 1 / (Gamma(1/3) * QPochhammer[1/9]^(1/3)) = 0.390040743840141117482137514... - Vaclav Kotesovec, Apr 22 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 22 2018 *)

CROSSREFS

Expansion of Product_{n>=1} 1/(1 - b^2*x^n)^(1/b): A000041 (b=1), A067855 (b=2), this sequence (b=3).

Cf. A303348.

Sequence in context: A141041 A079753 A137969 * A337467 A318041 A054419

Adjacent sequences:  A303346 A303347 A303348 * A303350 A303351 A303352

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 22 2018

STATUS

approved

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Last modified July 29 23:58 EDT 2021. Contains 346346 sequences. (Running on oeis4.)