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A301873 Expansion of Product_{k>=1} 1/(1 - x^k)^A007437(k). 3
1, 1, 5, 12, 36, 80, 215, 476, 1154, 2539, 5772, 12417, 27146, 57111, 120822, 249389, 514201, 1041684, 2103211, 4189502, 8306632, 16296337, 31803839, 61530913, 118413823, 226200319, 429857982, 811633548, 1524828119, 2848379512, 5295550209 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Euler transform of A007437.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ exp(2^(7/4) * Pi * Zeta(3)^(1/4) * n^(3/4) / (3^(5/4) * 5^(1/4)) + sqrt(5*Zeta(3)*n/6)/2 - (7*Pi * 5^(1/4) / (2^(15/4) * 3^(7/4) * Zeta(3)^(1/4)) + 5^(5/4) * Zeta(3)^(3/4) / (2^(15/4) * 3^(3/4) * Pi)) * n^(1/4) + (17*Zeta(3))/(72*Pi^2) + 23/576) * A^(1/4) * Zeta(3)^(23/192) / (2^(307/192) * 15^(23/192) * n^(119/192)), where A is the Glaisher-Kinkelin constant A074962.

MATHEMATICA

nmax = 40; CoefficientList[Series[Exp[Sum[Sum[(DivisorSigma[1, k] + DivisorSigma[2, k]) * x^(j*k) / (2*j), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)

CROSSREFS

Cf. A007437, A301874.

Sequence in context: A294654 A229043 A185699 * A077918 A300534 A297909

Adjacent sequences:  A301870 A301871 A301872 * A301874 A301875 A301876

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 28 2018

STATUS

approved

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Last modified April 4 20:25 EDT 2020. Contains 333229 sequences. (Running on oeis4.)