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A139415 Number of preferential arrangements (or hierarchical orderings) on the disconnected graphs on n unlabeled nodes. 1
0, 0, 2, 8, 40, 208, 1408, 12224, 157312, 3478528, 147761664, 12592434176, 2112188653568, 680441850810368, 415073848421801984, 476853486273606582272, 1030736815796444156755968, 4196432048875514376435007488, 32243698461915435195120257335296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = A000719(n)*A011782(n). Also A000088(n) = A001349(n) + A000719(n) and therefore A000088(n)*A011782(n) = A001349(n)*A011782(n) + A000719(n)*A011782(n) = A136722(n) + a(n).

EXAMPLE

For n=3 we have A139415(3) = 8 because:

There A000719 (3)=2 disconnected graphs for n=3 unlabeled elements:

Three disconnected points

o o o

and

one point plus a two-point chain

o o-o.

The three disconnected points give us 011782(3) = 4 arrangements:

o o o,

-----

o

o o,

-----

o o

o,

-----

o

o

o.

The point plus the two-point chain provides us with 4 arrangements:

o o-o,

-----

o-o

o,

-----

o

o-o,

-----

o

|

o o.

This gives us 8 hierarchical orderings.

(See A136722 for the two connected graphs for n=3, these are the three-point chain and the triangle.)

CROSSREFS

Cf. A136722, A000719, A000088, A011782.

Sequence in context: A154626 A003305 A076625 * A119817 A025570 A227081

Adjacent sequences:  A139412 A139413 A139414 * A139416 A139417 A139418

KEYWORD

nonn

AUTHOR

Thomas Wieder, Apr 20 2008

EXTENSIONS

Offset corrected and more terms from Alois P. Heinz, Apr 21 2012

STATUS

approved

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Last modified April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)