A158952 Inverse Euler transform of the number of partitions in expanding space (A023881).
1, 2, 9, 67, 625, 7903, 117649, 2105342, 43048905, 1000976352, 25937424601, 743191207969, 23298085122481, 793763217701693, 29192928060852217, 1152939097060278256, 48661191875666868481, 2185919903971766191000
Offset: 1
Keywords
Examples
Let G(x) = Sum_{n>=0} A023881(n)*x^n then
G(x) = 1 + x + 3*x^2 + 12*x^3 + 82*x^4 + 725*x^5 + 8811*x^6 +...
G(x) = 1/[(1-x)*(1-x^2)^2*(1-x^3)^9*(1-x^4)^67*(1-x^5)^625*...].
Programs
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Mathematica
Table[Sum[DivisorSigma[d, d]*MoebiusMu[n/d], {d, Divisors[n]}]/n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 09 2019 *) -
PARI
{a(n)=(1/n)*sumdiv(n,d,sigma(d,d)*moebius(n/d))}
Formula
a(n) = (1/n)*Sum_{d|n} sigma(d,d)*moebius(n/d).
a(n) ~ n^(n-1). - Vaclav Kotesovec, Oct 09 2019