OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 1 + A246169 = 3.51754035263200389079535459..., c = 0.59875012586719098912050580024... - Vaclav Kotesovec, Oct 30 2017
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(
b(d)*d*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
end:
a:= n-> add(b(k)*binomial(n, k), k=0..n):
seq(a(n), n=0..50); # Alois P. Heinz, Feb 24 2015
MATHEMATICA
b[n_] := b[n] = If[n<2, n, Sum[b[n-k]*Sum[b[d]*d*(-1)^(k/d+1), {d, Divisors[k]}], {k, 1, n-1}]/(n-1)]; a[n_] := Sum[b[k]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 12 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 27 2011
STATUS
approved