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A292037 Expansion of Product_{k>=1} ((1 + x^(2*k-1)) / (1 - x^(2*k-1)))^k. 5
1, 2, 2, 6, 10, 16, 30, 46, 78, 124, 196, 306, 470, 724, 1086, 1644, 2438, 3608, 5304, 7734, 11232, 16196, 23270, 33206, 47250, 66846, 94232, 132280, 184966, 257720, 357768, 495090, 682702, 938760, 1286668, 1758708, 2397012, 3258340, 4417570, 5974204, 8059824 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A263140 and A035528 (with a(0)=1).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

FORMULA

a(n) ~ exp(-1/24 - Pi^4/(1344*Zeta(3)) + Pi^2 * n^(1/3) / (8*(7*Zeta(3))^(1/3)) + 3*(7*Zeta(3))^(1/3) * n^(2/3)/4) * A^(1/2) * (7*Zeta(3))^(11/72) / (2^(5/4) * sqrt(3*Pi) * n^(47/72)), where A is the Glaisher-Kinkelin constant A074962.

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[((1+x^(2*k-1))/(1-x^(2*k-1)))^k, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A035528, A080054, A263140, A292038.

Sequence in context: A077017 A181551 A127404 * A184842 A181409 A248800

Adjacent sequences:  A292034 A292035 A292036 * A292038 A292039 A292040

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 08 2017

STATUS

approved

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Last modified March 23 05:36 EDT 2019. Contains 321422 sequences. (Running on oeis4.)