A285382 Sum of entries in the last cycles of all permutations of [n].

1, 5, 25, 143, 942, 7074, 59832, 563688, 5858640, 66622320, 823055040, 10979133120, 157300375680, 2409321801600, 39290164300800, 679701862425600, 12433400027596800, 239791474805299200, 4863054420016128000, 103462238924835840000, 2304147629440419840000

Offset: 1

Author

Alois P. Heinz, Apr 20 2017

Keywords

• nonn

Comments

Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..449
• Wikipedia, Permutation

Crossrefs

Cf. A284816, A285424, A285439.

Column k=1 of A286231.

Programs

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 *)

Formula

Recursion: see Maple program.