A397079 Expansion of g.f. (Sum_{j>=1} x^j/(1-x^j))^2 * Product_{k>=1} 1/(1-x^k).

0, 0, 1, 5, 14, 33, 67, 127, 226, 382, 628, 993, 1541, 2327, 3468, 5054, 7297, 10350, 14568, 20210, 27854, 37940, 51381, 68891, 91910, 121575, 160092, 209282, 272447, 352434, 454197, 582065, 743347, 944657, 1196586, 1509043, 1897428, 2376287, 2967707, 3693102, 4583742

Offset

0,4

Links

Table of n, a(n) for n=0..40.

Formula

a(n) ~ sqrt(3) * exp(Pi*sqrt(2*n/3)) * (log(6*n/Pi^2) + 2*gamma)^2 / (8*Pi^2), where gamma is the Euler-Mascheroni constant A001620.

Mathematica

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

Crossrefs

Cf. A006128, A397077, A397078.

Sequence in context: A271993 A274324 A014302 * A038090 A094002 A188589

Adjacent sequences: A397076 A397077 A397078 * A397080 A397081 A397082

Keyword

nonn

Author

Vaclav Kotesovec, Jun 16 2026

Status

approved