OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
N. J. A. Sloane, Transforms
FORMULA
Moebius transform of A055890(n).
a(n) ~ d^n / n, d = 2.69832910647421123126399866618837... (see A246828). - Vaclav Kotesovec, Aug 25 2014
MAPLE
with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, add(add(d, d=divisors(j)) *b(n-j), j=1..n)/n) end: c:= proc(n) option remember; local j; add(c(j) *b(n-j), j=1..n-1)-n*b(n) end: a:= -proc(n) option remember; local d; `if`(n=0, 1, add(mobius(n/d)*c(d), d=divisors(n))/n) end: seq(a(n), n=1..40); # Alois P. Heinz, Sep 09 2008
# The function EulerInvTransform is defined in A358451.
a := -EulerInvTransform(n -> -combinat:-numbpart(n)):
seq(a(n), n = 1..31); # Peter Luschny, Nov 21 2022
MATHEMATICA
b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d, {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]; c[n_] := c[n] = Sum[c[j]*b[n-j], {j, 1, n-1}] - n*b[n]; a[n_] := -If[n == 0, 1, Sum[MoebiusMu[n/d]*c[d], {d, Divisors[n]}]/n]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Feb 24 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jul 20 2004
EXTENSIONS
More terms from Alois P. Heinz, Sep 09 2008
STATUS
approved