

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
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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 twopoint chain
o oo.
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 twopoint chain provides us with 4 arrangements:
o oo,

oo
o,

o
oo,

o

o o.
This gives us 8 hierarchical orderings.
(See A136722 for the two connected graphs for n=3, these are the threepoint 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



