OFFSET
2,3
LINKS
Alois P. Heinz, Rows n = 2..142, flattened
FORMULA
E.g.f.: exp(x*y)*(exp(exp(x)-1-x)-1). - Vladeta Jovovic, Jul 28 2003
EXAMPLE
The 15 set partitions of {1,2,3,4} consist of 4 partitions with 0 blocks of length 1 : {{1,2,3,4}},{{1,2},{3,4}},{{1,3},{2,4}},{{1,4},{2,3}},
4 partitions with 1 block of length 1 : {{1},{2,3,4}},{{1,2,3},{4}},{{1,2,4},{3}},{{1,3,4},{2}}
6 partitions with 2 blocks of length 1 : {{1},{2},{3,4}},{{1},{2,3},{4}},{{1},{2,4},{3}},{{1,2},{3},{4}},{{1,3},{2},{4}},{{1,4},{2},{3}}.
(There are no partitions with n-1 blocks of length 1 and 1 with n of them)
1;
1, 3;
4, 4, 6;
11, 20, 10, 10;
41, 66, 60, 20, 15;
162, 287, 231, 140, 35, 21;
...
MAPLE
with(combinat):
b:= proc(n, i) option remember; expand(`if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i-1)*`if`(i=1, x^j, 1), j=0..n/i))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n-2))(b(n$2)):
seq(T(n), n=2..16); # Alois P. Heinz, Mar 08 2015
MATHEMATICA
Table[Count[Count[ #, {_Integer}]&/@SetPartitions[n], # ]&/@Range[0, n-2], {n, 2, 10}]
CROSSREFS
KEYWORD
AUTHOR
Wouter Meeussen, Jul 27 2003
EXTENSIONS
More terms from Vladeta Jovovic, Jul 28 2003
STATUS
approved