|
Search: id:A109186
|
|
|
| A109186 |
|
Number of hierarchical orderings of n unlabeled elements where levels are clustered. Labeled analogue of A104525. |
|
+0
3
|
|
| 1, 5, 36, 340, 3968, 55045, 883578, 16092772, 327632793, 7369013917, 181373908752, 4847134062319, 139729893353690, 4320778186663065, 142630863311312977, 5005242986601625051, 186036975046460920033
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
|
|
LINKS
|
Thomas Wieder, Discussion of A109186
Thomas Wieder, Home Page.
|
|
FORMULA
|
Generating function = exp(-(-1+exp(exp(z)-1))/(-2+exp(exp(z)-1)))-1.
|
|
EXAMPLE
|
a(2) = 5 because [a_{1}a_{2}], [a_{1}]:[a_{2}], [a_{2}]:[a_{1}], [a_{1}]|[a_{2}], [a_{1}][a_{2}].
|
|
MAPLE
|
Test := [T, {T=Set(S, card>=1), S=Sequence(Set(U, card>=1), card>=1), U=Set(Z, card>=1)}, labeled]; seq(count(Test, size=j), j=1..20);
|
|
CROSSREFS
|
Cf. A075729, A104525.
Cf. A104525, A083355, A075729.
Sequence in context: A000806 A127132 A075744 this_sequence A099391 A008785 A081918
Adjacent sequences: A109183 A109184 A109185 this_sequence A109187 A109188 A109189
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Thomas Wieder (wieder.thomas(AT)t-online.de), Jun 21 2005, Mar 29 2008
|
|
|
Search completed in 0.002 seconds
|
