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A262380 Expansion of Product_{k>=1} 1/((1+x^k)*(1-x^k)^4). 2
1, 3, 10, 25, 62, 136, 293, 590, 1165, 2205, 4097, 7391, 13120, 22780, 38997, 65613, 109036, 178660, 289575, 463842, 735870, 1155717, 1799620, 2777795, 4254859, 6467115, 9761770, 14633605, 21799465, 32273399, 47506759, 69537814, 101252595, 146675875, 211451893 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..34.

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. 16.

FORMULA

a(n) ~ exp(sqrt(7*n/3)*Pi) * 7^(5/4) / (32 * 3^(5/4) * n^(7/4)).

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[1/((1 + x^k)*(1 - x^k)^4), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A002513 (m=2), A029863 (m=3), A261998.

Sequence in context: A034506 A067988 A297186 * A005674 A089100 A089117

Adjacent sequences:  A262377 A262378 A262379 * A262381 A262382 A262383

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 20 2015

STATUS

approved

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Last modified October 23 17:37 EDT 2020. Contains 337969 sequences. (Running on oeis4.)