OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..501
Wikipedia, Partition of a set
FORMULA
E.g.f.: exp((exp(x)-1)^3/3!).
a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling2(n,3*k)/(6^k * k!). - Seiichi Manyama, May 07 2022
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
*binomial(n-1, j-1)*Stirling2(j, 3), j=3..n))
end:
seq(a(n), n=0..25);
MATHEMATICA
a[n_] := a[n] = If[n == 0, 1, Sum[a[n - j] Binomial[n - 1, j -1] StirlingS2[j, 3], {j, 3, n}]];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 16 2020, after Alois P. Heinz *)
PROG
(PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 2)/(6^k*k!)); \\ Seiichi Manyama, May 07 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 14 2019
STATUS
approved