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A136723
Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.
2
1, 1, 3, 52, 2850, 393848, 125054832, 88260845008, 137304025714320, 469859118159233792, 3527181890877230433408, 57833314494643038031674112, 2060645597746315164145860149760, 158727775101107953869596632383822848, 26301662700662611321804753231934678909952
OFFSET
0,3
COMMENTS
Figure n3 demonstrates all 4*13=52 hierarchical orderings on n=3 connected points. In addition, the pink pictures describe the 10 cases where not all or no points are connected.
LINKS
Thomas Wieder, Figure n3
FORMULA
a(n) = A001187(n)*A000670(n);
EXAMPLE
There is A001187(2)=1 connected graph for n=2 labeled elements: The chain 1-2.
The chain gives us 3 hierarchical orderings:
1-2
1
|
2
2
|
1
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Thomas Wieder, Jan 19 2008; corrected Jan 19 2008
EXTENSIONS
Offset corrected by Alois P. Heinz, Dec 16 2014
STATUS
approved