OFFSET
0,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 1.964293016979213611214370656... and c = 0.8776048696248050091050307... . - Vaclav Kotesovec, Jun 23 2014
G.f.: x + x^2 + x^3 / Product_{n>=1} (1 - x^n)^a(n). - Ilya Gutkovskiy, May 08 2019
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1,
(add(add(d*a(d), d=divisors(j)) *b(n-j), j=1..n))/n)
end:
a:= n-> `if`(n<3, signum(n), b(n-3)):
seq(a(n), n=0..40);
MATHEMATICA
b[n_] := b[n] = If[n == 0, 1, (Sum[Sum[d*a[d], {d, Divisors[j]}]*b[n - j], {j, 1, n }])/n]; a[0] = 0; a[1] = a[2] = 1; a[n_] := b[n - 3]; Table[a[n], {n, 0, 39}] (* Jean-François Alcover, Aug 01 2013, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
Alois P. Heinz, Oct 18 2012
STATUS
approved