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%I #43 Apr 06 2016 09:12:06
%S 0,0,0,1,10,74,504,3383,23004,160444,1154524,8594072,66243532,
%T 528776232,4369175522,37343891839,329883579768,3008985817304,
%U 28312886239136,274561779926323,2741471453779930,28159405527279326,297291626845716642,3223299667111201702
%N Total number of inversions in all set partitions of [n].
%C Each set partition is written as a sequence of blocks, ordered by the smallest elements in the blocks.
%H Alois P. Heinz, <a href="/A264082/b264082.txt">Table of n, a(n) for n = 0..210</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics)">Inversion (discrete mathematics)</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F a(n) = Sum_{k>0} k * A125810(n,k).
%e a(3) = 1: one inversion in 13|2.
%e 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.
%Y Cf. A001809, A125810, A189052, A211606, A216239, A271370.
%K nonn
%O 0,5
%A _Alois P. Heinz_, Apr 03 2016
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