Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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