A285232 Number of entries in the fourth cycles of all permutations of [n].

1, 12, 119, 1177, 12217, 135302, 1606446, 20450052, 278604252, 4051377504, 62702222112, 1029832270848, 17899305402240, 328353314855040, 6341705227082880, 128655706986282240, 2735782096305749760, 60855815849067648000, 1413487524282196608000

Offset

4,2

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 = 4..449

Wikipedia, Permutation

Formula

a(n) = A185105(n,4).

a(n) ~ n!*n/16. - Vaclav Kotesovec, Apr 25 2017

Maple

a:= proc(n) option remember; `if`(n<5, [0$4, 1][n+1],
      ((n-2)*(3*n^2-13*n+6)*a(n-1)-(3*n^4-26*n^3+76*n^2
      -81*n+16)*a(n-2)+(n-3)^4*n*a(n-3))/((n-1)*(n-4)))
    end:
seq(a(n), n=4..30);

Mathematica

a[3]=0; a[4]=1; a[5]=12; a[n_] := a[n] = ((n-2)(3n^2 - 13n + 6) a[n-1] - ( 3n^4 - 26n^3 + 76n^2 - 81n + 16)a[n-2]+(n-3)^4 n a[n-3])/((n-1)(n-4));
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Jun 01 2018, from Maple *)

Crossrefs

Column k=4 of A185105.

Sequence in context: A163950 A025132 A001712 * A077251 A289542 A075622

Adjacent sequences: A285229 A285230 A285231 * A285233 A285234 A285235

Keyword

nonn

Author

Alois P. Heinz, Apr 15 2017

Status

approved