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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 (list; graph; refs; listen; history; text; internal format)
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 13|2.

a(4) = 10: one inversion in each of 124|3, 13|24, 13|2|4, 1|24|3, and two inversions in each of 134|2, 14|23, 14|2|3.

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

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Last modified September 27 16:20 EDT 2020. Contains 337383 sequences. (Running on oeis4.)