|
| |
|
|
A032032
|
|
Number of ways to partition n labeled elements into sets of sizes of at least 2 and order the sets.
|
|
3
| |
|
|
1, 0, 1, 1, 7, 21, 141, 743, 5699, 42241, 382153, 3586155, 38075247, 428102117, 5257446533, 68571316063, 959218642651, 14208251423433, 223310418094785, 3699854395380371, 64579372322979335, 1182959813115161773, 22708472725269799933
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
LINKS
| C. G. Bower, Transforms (2)
Index entries for related partition-counting sequences
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 245
|
|
|
FORMULA
| "AIJ" (ordered, indistinct, labeled) transform of 0, 1, 1, 1...
E.g.f.: 1/(2+x-e^x).
a(n) = n! * sum(k=1..n, sum(j=0..k, binomial(k,j) *stirling2(n-k+j,j) *j!/(n-k+j)! *(-1)^(k-j))); a(0)=1. - From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Feb 01 2011
|
|
|
MAPLE
| spec := [ B, {B=Sequence(Set(Z, card>1))}, labeled ]; [seq(combstruct[count](spec, size=n), n=0..30)];
|
|
|
CROSSREFS
| Sequence in context: A001693 A061961 A028248 * A084711 A183938 A060146
Adjacent sequences: A032029 A032030 A032031 * A032033 A032034 A032035
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
|
| |
|
|
