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

1,2

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = (1/n)*Sum_{d|n} sigma(d,d)*moebius(n/d).

a(n) ~ n^(n-1). - Vaclav Kotesovec, Oct 09 2019

Example

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*...].

Mathematica

Table[Sum[DivisorSigma[d, d]*MoebiusMu[n/d], {d, Divisors[n]}]/n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 09 2019 *)

Prog

(PARI) {a(n)=(1/n)*sumdiv(n, d, sigma(d, d)*moebius(n/d))}

Crossrefs

Cf. A023881, A158947.

Sequence in context: A243281 A091795 A319286 * A324167 A376125 A296793

Adjacent sequences: A158949 A158950 A158951 * A158953 A158954 A158955

Keyword

nonn

Author

Paul D. Hanna, Mar 31 2009

Status

approved