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A212397 Denominator of the average number of move operations required by an insertion sort of n (distinct) elements.

%I A212397 #21 May 29 2018 09:25:03
%S A212397 1,1,2,6,6,30,5,35,140,1260,1260,13860,13860,180180,180180,180180,
%T A212397 360360,6126120,2042040,38798760,7759752,2586584,2586584,59491432,
%U A212397 178474296,4461857400,4461857400,40156716600,40156716600,1164544781400,1164544781400
%N A212397 Denominator of the average number of move operations required by an insertion sort of n (distinct) elements.
%C A212397 The average number of move operations is 1/n! times the number of move operations required to sort all permutations of [n] (A212395), assuming that each permutation is equiprobable.
%H A212397 Alois P. Heinz, <a href="/A212397/b212397.txt">Table of n, a(n) for n = 0..1000</a>
%H A212397 Wikipedia, <a href="https://en.wikipedia.org/wiki/Insertion_sort">Insertion sort</a>
%H A212397 <a href="/index/So#sorting">Index entries for sequences related to sorting</a>
%F A212397 a(n) = denominator of A212395(n)/A000142(n).
%p A212397 b:= proc(n) option remember;
%p A212397       `if`(n=0, 0, b(n-1)*n + (n-1)! * (n-1)*(n+4)/2)
%p A212397     end:
%p A212397 a:= n-> denom(b(n)/n!):
%p A212397 seq(a(n), n=0..30);
%t A212397 a[n_] := Denominator[n (n + 7)/4 - 2 HarmonicNumber[n]];
%t A212397 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 29 2018, from 2nd formula in A212396 *)
%Y A212397 Numerators are in A212396.
%Y A212397 Cf. A000142, A212395.
%K A212397 nonn,frac
%O A212397 0,3
%A A212397 _Alois P. Heinz_, May 14 2012