A285795 Sum of the second entries in all cycles of all permutations of [n].

0, 0, 2, 13, 83, 582, 4554, 39672, 382248, 4044240, 46663920, 583554240, 7865622720, 113711230080, 1755484617600, 28828769356800, 501858148377600, 9232213174732800, 178968924600883200, 3646603415927808000, 77916767838981120000, 1742147265551616000000

Offset: 0

Author

Alois P. Heinz, Apr 26 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) = 13 because the sum of the second entries in all cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 2+3+2+3+3+0 = 13.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..449
• Wikipedia, Permutation

Crossrefs

Column k=2 of A285793.

Cf. A001008, A002805.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, n*(n-1),
     ((2*n^2+3*n-1)*a(n-1)-(n-1)*n*(n+2)*a(n-2))/(n+1))
    end:
seq(a(n), n=0..25);

Mathematica

Flatten[{0, Table[n! * (2*(n+1)*HarmonicNumber[n] - n - 3)/4, {n, 1, 25}]}] (* Vaclav Kotesovec, Apr 29 2017 *)