cp's OEIS Frontend

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

%I A285232 #11 Jun 01 2018 07:50:06
%S A285232 1,12,119,1177,12217,135302,1606446,20450052,278604252,4051377504,
%T A285232 62702222112,1029832270848,17899305402240,328353314855040,
%U A285232 6341705227082880,128655706986282240,2735782096305749760,60855815849067648000,1413487524282196608000
%N A285232 Number of entries in the fourth cycles of all permutations of [n].
%C A285232 Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
%H A285232 Alois P. Heinz, <a href="/A285232/b285232.txt">Table of n, a(n) for n = 4..449</a>
%H A285232 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A285232 a(n) = A185105(n,4).
%F A285232 a(n) ~ n!*n/16. - _Vaclav Kotesovec_, Apr 25 2017
%p A285232 a:= proc(n) option remember; `if`(n<5, [0$4, 1][n+1],
%p A285232       ((n-2)*(3*n^2-13*n+6)*a(n-1)-(3*n^4-26*n^3+76*n^2
%p A285232       -81*n+16)*a(n-2)+(n-3)^4*n*a(n-3))/((n-1)*(n-4)))
%p A285232     end:
%p A285232 seq(a(n), n=4..30);
%t A285232 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 A285232 Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, Jun 01 2018, from Maple *)
%Y A285232 Column k=4 of A185105.
%K A285232 nonn
%O A285232 4,2
%A A285232 _Alois P. Heinz_, Apr 15 2017