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A136722 Number of preferential arrangements (or hierarchical orderings) on the connected graphs on n unlabeled nodes. 2
1, 1, 2, 8, 48, 336, 3584, 54592, 1422976, 66836480, 5998884352, 1030861378560, 335994532814848, 206175878632321024, 237596569295651315712, 514414692643000188272640, 2096154545790162572944244736, 16113456361117058761983824232448, 234269143891823701379016369973493760 (list; graph; refs; listen; history; text; internal format)
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: A228568 A007170 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

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Last modified October 21 14:57 EDT 2018. Contains 316424 sequences. (Running on oeis4.)