|
|
A285382
|
|
Sum of entries in the last cycles of all permutations of [n].
|
|
5
|
|
|
1, 5, 25, 143, 942, 7074, 59832, 563688, 5858640, 66622320, 823055040, 10979133120, 157300375680, 2409321801600, 39290164300800, 679701862425600, 12433400027596800, 239791474805299200, 4863054420016128000, 103462238924835840000, 2304147629440419840000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
|
|
LINKS
|
|
|
FORMULA
|
Recursion: see Maple program.
|
|
EXAMPLE
|
a(3) = 25 because the sum of the entries in the last cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 6+6+3+2+5+3 = 25.
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n<3, n*(3*n-1)/2,
((2*n^2+3*n-1)*a(n-1)-(n+2)*(n-1)*n*a(n-2))/(n+1))
end:
seq(a(n), n=1..25);
|
|
MATHEMATICA
|
Table[n! * (n-1 + 2*(n+1)*HarmonicNumber[n])/4, {n, 1, 25}] (* Vaclav Kotesovec, Apr 29 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|