A261648 - OEIS

A261648

Expansion of Product_{k>=0} ((1+x^(2*k+1))/(1-x^(2*k+1)))^5.

1, 10, 50, 180, 550, 1512, 3820, 9040, 20310, 43670, 90472, 181540, 354180, 674040, 1254640, 2289104, 4101430, 7228020, 12546030, 21473940, 36281656, 60565920, 99974140, 163297520, 264110180, 423211938, 672244600, 1059013320, 1655274320, 2568068120

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OFFSET

0,2

COMMENTS

In general, if j > 0 and g.f. = Product_{k>=0} ((1 + x^(2*k+1))/(1 - x^(2*k+1)))^j, then a(n) ~ exp(Pi*sqrt(j*n/2)) * j^(1/4) / (2^(j/2 + 7/4) * n^(3/4)).

LINKS

Table of n, a(n) for n=0..29.

Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 11.

FORMULA

a(n) ~ exp(Pi*sqrt(5*n/2)) * 5^(1/4) / (16 * 2^(1/4) * n^(3/4)).

MATHEMATICA

nmax=60; CoefficientList[Series[Product[((1+x^(2*k+1))/(1-x^(2*k+1)))^5, {k, 0, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A080054 (j=1), A007096 (j=2), A261647 (j=3), A014969 (j=4), A014970 (j=6), A014972 (j=8), A103261 (j=10).

Sequence in context: A008413 A006542 A237655 * A086462 A201830 A192019

Adjacent sequences: A261645 A261646 A261647 * A261649 A261650 A261651

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 28 2015

STATUS

approved