OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..386
MAPLE
b:= proc(n) option remember; local r, f, g;
if n=0 then 1 else r, f, g:=$0..2;
while f<=n do r, f, g:= r+(f-1)!*
b(n-f)*binomial(n-1, f-1), f+g, g+1
od; r fi
end:
a:= n-> add(b(j)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..20);
MATHEMATICA
b[n_] := b[n] = Module[{r, f, g}, If[n == 0, 1, {r, f, g} = {0, 1, 2}; While[f <= n, {r, f, g} = {r + (f - 1)!*b[n - f]*Binomial[n - 1, f - 1], f + g, g + 1}]; r]];
a[0] = 1; a[n_] := Sum[b[j]*n^(n - j)*Binomial[n - 1, j - 1], {j, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jun 15 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 10 2018
STATUS
approved