OFFSET
0,3
COMMENTS
All terms are even.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..424
MAPLE
g:= proc(n) option remember; `if`(n<2, 1,
add(binomial(n, k)*g(k), k=0..n-1))
end:
b:= proc(n, i, p) option remember;
`if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
`if`(i>n, 0, b(n-i, i-1, p+1)*binomial(n, i))))
end:
a:= n-> g(n)-b(n$2, 0):
seq(a(n), n=0..25);
MATHEMATICA
g[n_] := g[n] = If[n<2, 1, Sum[Binomial[n, k]*g[k], {k, 0, n-1}]]; b[n_, i_, p_] := b[n, i, p] = If[i*(i+1)/2<n, 0, If[n==0, p!, b[n, i-1, p] + If[i>n, 0, b[n-i, i-1, p+1]*Binomial[n, i]]]]; a[n_] := g[n] - b[n, n, 0]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 09 2015
STATUS
approved