

A264082


Total number of inversions in all set partitions of [n].


4



0, 0, 0, 1, 10, 74, 504, 3383, 23004, 160444, 1154524, 8594072, 66243532, 528776232, 4369175522, 37343891839, 329883579768, 3008985817304, 28312886239136, 274561779926323, 2741471453779930, 28159405527279326, 297291626845716642, 3223299667111201702
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OFFSET

0,5


COMMENTS

Each set partition is written as a sequence of blocks, ordered by the smallest elements in the blocks.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..210
Wikipedia, Inversion (discrete mathematics)
Wikipedia, Partition of a set


FORMULA

a(n) = Sum_{k>0} k * A125810(n,k).


EXAMPLE

a(3) = 1: one inversion in 132.
a(4) = 10: one inversion in each of 1243, 1324, 1324, 1243, and two inversions in each of 1342, 1423, 1423.


CROSSREFS

Cf. A001809, A125810, A189052, A211606, A216239, A271370.
Sequence in context: A044578 A309884 A279284 * A103434 A119167 A233100
Adjacent sequences: A264079 A264080 A264081 * A264083 A264084 A264085


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Apr 03 2016


STATUS

approved



