|
|
A212397
|
|
Denominator of the average number of move operations required by an insertion sort of n (distinct) elements.
|
|
3
|
|
|
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
|
|
|
FORMULA
|
|
|
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);
|
|
MATHEMATICA
|
a[n_] := Denominator[n (n + 7)/4 - 2 HarmonicNumber[n]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|