OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..30
Wikipedia, Partition of a set
FORMULA
a(n) = (n!)^n * [x^n] exp(Sum_{k>=1} x^k / (k!)^n). - Ilya Gutkovskiy, Jul 12 2020
EXAMPLE
a(2) = 3: 1234, 12|34, 14|23.
a(3) = 64: 123456789, 123456|789, 123459|678, 123468|579, ... , 159|267|348, 168|279|345, 189|267|345.
MAPLE
b:= proc(n, k) option remember; `if`(k*n=0, 1, add(
binomial(n, j)^k*(n-j)*b(j, k), j=0..n-1)/n)
end:
a:= n-> b(n$2):
seq(a(n), n=0..12);
MATHEMATICA
b[n_, k_] := b[n, k] = If[k*n == 0, 1, Sum[Binomial[n, j]^k*(n-j)*b[j, k], {j, 0, n-1}]/n];
a[n_] := b[n, n];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, May 27 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 14 2016
STATUS
approved