A212397 - OEIS

A212397

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

1, 1, 2, 6, 6, 30, 5, 35, 140, 1260, 1260, 13860, 13860, 180180, 180180, 180180, 360360, 6126120, 2042040, 38798760, 7759752, 2586584, 2586584, 59491432, 178474296, 4461857400, 4461857400, 40156716600, 40156716600, 1164544781400, 1164544781400

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Insertion sort

Index entries for sequences related to sorting

FORMULA

a(n) = denominator of A212395(n)/A000142(n).

MAPLE

b:= proc(n) option remember;

`if`(n=0, 0, b(n-1)*n + (n-1)! * (n-1)*(n+4)/2)

end:

a:= n-> denom(b(n)/n!):

seq(a(n), n=0..30);