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A158952 Inverse Euler transform of the number of partitions in expanding space (A023881). 1
1, 2, 9, 67, 625, 7903, 117649, 2105342, 43048905, 1000976352, 25937424601, 743191207969, 23298085122481, 793763217701693, 29192928060852217, 1152939097060278256, 48661191875666868481, 2185919903971766191000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Sequence in context: A243281 A091795 A319286 * A324167 A296793 A366336
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 31 2009
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)