A397077 Expansion of g.f. (Sum_{j>=1} x^j/(1-x^j))^2 * Product_{k>=1} (1+x^k)/(1-x^k).

0, 0, 1, 6, 20, 54, 126, 268, 533, 1002, 1810, 3150, 5326, 8774, 14144, 22348, 34716, 53084, 80051, 119174, 175374, 255316, 368062, 525744, 744646, 1046334, 1459402, 2021408, 2781580, 3804042, 5172132, 6993472, 9406809, 12590120, 16771020, 22239580, 29364454, 38612298

Offset

0,4

Comments

Convolution of A305082 and A006128.

Links

Table of n, a(n) for n=0..37.

Formula

a(n) ~ exp(Pi*sqrt(n)) * (log(4*n/Pi^2) + 2*gamma)^2 / (8*Pi^2), where 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)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A305102, A397078, A397079.

Cf. A305082, A006128.

Sequence in context: A055909 A036596 A298408 * A038091 A027993 A396927

Adjacent sequences: A397074 A397075 A397076 * A397078 A397079 A397080

Keyword

nonn

Author

Vaclav Kotesovec, Jun 16 2026

Status

approved