A136723 Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n labeled nodes.

1, 1, 3, 52, 2850, 393848, 125054832, 88260845008, 137304025714320, 469859118159233792, 3527181890877230433408, 57833314494643038031674112, 2060645597746315164145860149760, 158727775101107953869596632383822848, 26301662700662611321804753231934678909952

Offset: 0

Author

Thomas Wieder, Jan 19 2008; corrected Jan 19 2008

Keywords

• easy
• nonn

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.

Examples

			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
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..76
• Thomas Wieder, Figure n3

Crossrefs

Cf. A001187, A000670, A136722, A034691, A075729.

Formula

a(n) = A001187(n)*A000670(n);

Extensions

Offset corrected by Alois P. Heinz, Dec 16 2014