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

0,3

Comments

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

Links

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

Wikipedia, Permutation

Example

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.

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 *)

Crossrefs

Column k=2 of A285793.

Cf. A001008, A002805.

Sequence in context: A317892 A079752 A156018 * A134148 A164035 A382919

Adjacent sequences: A285792 A285793 A285794 * A285796 A285797 A285798

Keyword

nonn

Author

Alois P. Heinz, Apr 26 2017

Status

approved