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A300579 Expansion of Product_{k>=1} 1/(1 - 3^(k-1)*x^k). 13
1, 1, 4, 13, 49, 157, 589, 1885, 6826, 22378, 78754, 256630, 904711, 2934247, 10133851, 33287620, 113522089, 370582069, 1262300701, 4110883510, 13869616495, 45364050184, 151708228636, 494743296757, 1654133919475, 5379427446952, 17858926956532, 58219580395822 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In general, if g.f. = Product_{k>=1} 1/(1 - d^(k-1)*x^k), where d > 1, then a(n) ~ sqrt(d-1) * polylog(2, 1/d)^(1/4) * d^(n - 1/2) * exp(2*sqrt(polylog(2, 1/d)*n)) / (2*sqrt(Pi)*n^(3/4)).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

FORMULA

a(n) ~ polylog(2, 1/3)^(1/4) * 3^(n - 1/2) * exp(2*sqrt(polylog(2, 1/3)*n)) / (sqrt(2*Pi) * n^(3/4)), where polylog(2, 1/3) = 0.36621322997706348761674629...

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[1/(1 - 3^(k-1)*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A075900.

Sequence in context: A149450 A297591 A294298 * A180007 A338862 A097948

Adjacent sequences:  A300576 A300577 A300578 * A300580 A300581 A300582

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 09 2018

STATUS

approved

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)