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A261451 Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(k+1). 4
1, 4, 14, 44, 124, 328, 824, 1980, 4590, 10320, 22584, 48268, 101016, 207432, 418704, 832032, 1629764, 3150280, 6014998, 11354084, 21204488, 39206168, 71811256, 130369900, 234704360, 419195412, 743085912, 1307823672, 2286094704, 3970174648, 6852048368 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Convolution of A005380 and A219555.
LINKS
FORMULA
a(n) ~ (7*Zeta(3))^(13/36) * exp(1/12 - Pi^4/(336*Zeta(3)) + Pi^2 * n^(1/3) / (2^(5/3) * (7*Zeta(3))^(1/3)) + 3/2 * ((7*Zeta(3))/2)^(1/3) * n^(2/3)) / (A * 2^(35/18) * 3^(1/2) * Pi * n^(31/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(k+1), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A037528 A292718 A212688 * A084613 A099063 A057223
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 19 2015
STATUS
approved

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Last modified May 25 15:35 EDT 2024. Contains 372797 sequences. (Running on oeis4.)