A285232 - OEIS

%I #11 Jun 01 2018 07:50:06

%S 1,12,119,1177,12217,135302,1606446,20450052,278604252,4051377504,

%T 62702222112,1029832270848,17899305402240,328353314855040,

%U 6341705227082880,128655706986282240,2735782096305749760,60855815849067648000,1413487524282196608000

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

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

%H Alois P. Heinz, <a href="/A285232/b285232.txt">Table of n, a(n) for n = 4..449</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

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

%F a(n) ~ n!*n/16. - _Vaclav Kotesovec_, Apr 25 2017

%p a:= proc(n) option remember; `if`(n<5, [0$4, 1][n+1],

%p       ((n-2)*(3*n^2-13*n+6)*a(n-1)-(3*n^4-26*n^3+76*n^2

%p       -81*n+16)*a(n-2)+(n-3)^4*n*a(n-3))/((n-1)*(n-4)))

%p     end:

%p seq(a(n), n=4..30);

%t 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));

%t Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, Jun 01 2018, from Maple *)

%Y Column k=4 of A185105.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Apr 15 2017