OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..800
EXAMPLE
a(0) = 1: {}.
a(1) = 1: {a}.
a(2) = 2: {aa}, {ab}.
a(3) = 6: {a,aa}, {a,ab}, {aaa}, {aab}, {aba}, {abc}.
MAPLE
g:= proc(n) option remember;
`if`(n<2, 1, g(n-1)+(n-1)*g(n-2))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(g(i), j), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..35);
MATHEMATICA
g[n_] := g[n] = If[n < 2, 1, g[n - 1] + (n - 1)*g[n - 2]];
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1]* Binomial[g[i], j], {j, 0, n/i}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 06 2018, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 30 2017
STATUS
approved