A377585 E.g.f.: exp(Sum_{k>=1} A057660(k) * x^k).

1, 1, 7, 61, 577, 7381, 96511, 1619857, 28368481, 560654857, 12100090231, 282510616741, 7098784113697, 190647458125021, 5461212525476527, 165494332157561401, 5306572876379307841, 178898083900878623377, 6336492991778941139431, 234867483921621706900237, 9096385945218131126509441

Offset: 0

Author

Vaclav Kotesovec, Nov 02 2024

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A057660.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Exp[Sum[DivisorSigma[2, k^2]/DivisorSigma[1, k^2]*x^k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!

Formula

a(n) ~ 3^(1/4) * zeta(3)^(1/8) * exp(sqrt(Pi)*n^(1/4)/(6^(3/2)*zeta(3)^(1/4)) + 2^(5/2)*zeta(3)^(1/4)*n^(3/4)/sqrt(3*Pi) - n) * n^(n - 1/8) / (2^(3/4) * Pi^(1/4)).