A397081 Expansion of g.f. (Sum_{j>=1} x^j/(1-x^j))^2 * Product_{k>=1} (1+x^k)^k.

0, 0, 1, 5, 14, 35, 78, 164, 331, 638, 1203, 2197, 3937, 6915, 11945, 20319, 34102, 56541, 92680, 150391, 241688, 385056, 608403, 954033, 1485268, 2296836, 3529317, 5390769, 8187309, 12367754, 18587283, 27798372, 41381012, 61326589, 90499658, 133005971, 194712792, 283976310

Offset

0,4

Links

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

Formula

a(n) ~ exp(3^(4/3) * zeta(3)^(1/3) * n^(2/3) / 2^(4/3)) * (log(2*n/(3*zeta(3))) + 3*gamma)^2 / (27 * 2^(1/12) * sqrt(Pi*zeta(3))), 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)^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A397040, A397078, A397080, A397082.

Sequence in context: A001215 A335651 A066767 * A027983 A227200 A142585

Adjacent sequences: A397078 A397079 A397080 * A397082 A397083 A397084

Keyword

nonn

Author

Vaclav Kotesovec, Jun 16 2026

Status

approved