A136722 Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n unlabeled nodes.

1, 1, 2, 8, 48, 336, 3584, 54592, 1422976, 66836480, 5998884352, 1030861378560, 335994532814848, 206175878632321024, 237596569295651315712, 514414692643000188272640, 2096154545790162572944244736, 16113456361117058761983824232448, 234269143891823701379016369973493760

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n)=A001349(n)*A011782(n).

Example

There are A001349(3)=2 connected graphs for n=3 unlabeled elements:
The chain
o-o-o
and the triangle
. o
/..\
o - o.
There are a(3)=8 hierarchical orders on these two graphs.
The chain gives us 6 orderings:
o-o-o
o
|
o-o
. o
/..\
o . o
o . o
.\./
. o
o-o
|
o
o
|
o
|
o
The triangle gives us two orderings:
. o
/..\
o - o
o - o
\../
. o

Crossrefs

Cf. A001349, A011782, A136723, A034691, A075729.

Sequence in context: A007170 A355488 A171455 * A085615 A054726 A003576

Adjacent sequences: A136719 A136720 A136721 * A136723 A136724 A136725

Keyword

easy,nonn

Author

Thomas Wieder, Jan 19 2008

Extensions

More terms from Alois P. Heinz, Apr 21 2012

Status

approved