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A086659
T(n,k) counts the set partitions of n containing k-1 blocks of length 1.
4
1, 1, 3, 4, 4, 6, 11, 20, 10, 10, 41, 66, 60, 20, 15, 162, 287, 231, 140, 35, 21, 715, 1296, 1148, 616, 280, 56, 28, 3425, 6435, 5832, 3444, 1386, 504, 84, 36, 17722, 34250, 32175, 19440, 8610, 2772, 840, 120, 45, 98253, 194942, 188375, 117975, 53460, 18942, 5082, 1320, 165, 55
OFFSET
2,3
LINKS
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
Row sums = Bell[n]-1 (A058692), first column=A000296, main diagonal = triangular numbers A000217.
Sequence in context: A100692 A360724 A089640 * A265887 A345264 A344465
KEYWORD
nonn,tabl,easy
AUTHOR
Wouter Meeussen, Jul 27 2003
EXTENSIONS
More terms from Vladeta Jovovic, Jul 28 2003
STATUS
approved