A397082 Expansion of g.f. (Sum_{j>=1} x^j/(1-x^j))^2 * Product_{k>=1} 1/(1-x^k)^k.

0, 0, 1, 5, 15, 40, 95, 214, 457, 937, 1865, 3602, 6807, 12585, 22875, 40865, 72009, 125127, 214930, 364934, 613515, 1021345, 1685654, 2758549, 4480070, 7222057, 11563479, 18393005, 29078137, 45699763, 71426896, 111042494, 171763067, 264397434, 405116786, 617968699, 938655535

Offset

0,4

Links

Table of n, a(n) for n=0..36.

Formula

a(n) ~ exp(1/12 + 3*zeta(3)^(1/3)*n^(2/3)/2^(2/3)) * (log(n/(2*zeta(3))) + 3*gamma)^2 / (A * 2^(35/36) * 3^(5/2) * sqrt(Pi) * zeta(3)^(17/36) * n^(1/36)), where A is the Glaisher-Kinkelin constant A074962 and gamma is the Euler-Mascheroni constant A001620.

Mathematica

nmax = 40; CoefficientList[Series[Sum[x^j/(1-x^j), {j, 1, nmax}]^2 / Product[(1-x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A397039, A397079, A397080, A397081.

Sequence in context: A132985 A022570 A152881 * A000333 A291225 A054888

Adjacent sequences: A397079 A397080 A397081 * A397083 A397084 A397088

Keyword

nonn

Author

Vaclav Kotesovec, Jun 16 2026

Status

approved