OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
Wikipedia, Partition of a set
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, `if`(k=0 or k>n, 0,
add(b(n-j, k)*binomial(n-1, j-1)*Stirling2(j, k), j=k..n)))
end:
a:= n-> add(b(n, k), k=0..n):
seq(a(n), n=0..23);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == 0, 1, If[k == 0 || k > n, 0, Sum[b[n-j, k]* Binomial[n - 1, j - 1] StirlingS2[j, k], {j, k, n}]]];
a[n_] := Sum[b[n, k], {k, 0, n}];
a /@ Range[0, 23] (* Jean-François Alcover, May 05 2020, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 02 2019
STATUS
approved