OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..750
N. J. A. Sloane, Transforms
FORMULA
Inverse Moebius transform of A000055.
a(n) ~ c * d^n / n^(5/2), where d = A051491 = 2.9557652856519949747148..., c = A086308 = 0.53494960614230701455... . - Vaclav Kotesovec, Aug 25 2014
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n<=1, n,
(add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
end:
g:= proc(n) option remember; local k; `if`(n=0, 1, b(n)-
(add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2)
end:
a:= n-> `if`(n=0, 1, add(g(d), d=divisors(n))):
seq(a(n), n=0..35); # Alois P. Heinz, May 18 2013
MATHEMATICA
b[n_] := b[n] = If[n <= 1, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n-1}]/(n-1)]; g[n_] := g[n] = If[n==0, 1, b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[Mod[n, 2]==0, b[n/2], 0])/2]; a[n_] := If[n==0, 1, Sum[ g[d], {d, Divisors[n]}]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Feb 19 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Oct 15 1998.
STATUS
approved