cp's OEIS Frontend

A229244 Number of n-permutations such that at least one cycle has size ceiling(n/2).

%I A229244 #14 May 23 2014 12:01:38
%S A229244 1,1,3,9,40,200,1260,8820,72576,653184,6652800,73180800,889574400,
%T A229244 11564467200,163459296000,2451889440000,39520825344000,
%U A229244 671854030848000,12164510040883200,231125690776780800,4644631106519040000,97537253236899840000,2154334728240414720000,49549698749529538560000,1193170003333152768000000
%N A229244 Number of n-permutations such that at least one cycle has size ceiling(n/2).
%F A229244 For odd n,  a(2m+1)= binomial(2m+1,m+1)*m!^2.
%F A229244 For even n, a(2m) = binomial(2m,m)*(m-1)!*(m!-(m-1)!) + (2m)!/(2*m^2).
%F A229244 Conjecture: (n+1)*a(n) +(-3*n+1)*a(n-1) -(n-2)*(n^2-2*n-1)*a(n-2) +(n-2)*(n-3)^2*a(n-3)=0. - _R. J. Mathar_, May 23 2014
%e A229244 a(4) = 9 because we have:
%e A229244 1: (1)(2)(4,3)
%e A229244 2: (1)(3,2)(4)
%e A229244 3: (1)(4,2)(3)
%e A229244 4: (2,1)(3)(4)
%e A229244 5: (2,1)(4,3)
%e A229244 6: (3,1)(2)(4)
%e A229244 7: (3,1)(4,2)
%e A229244 8: (4,1)(2)(3)
%e A229244 9: (4,1)(3,2).
%t A229244 f[n_]:=If[EvenQ[n],Binomial[n,n/2](n/2-1)!((n/2)!-(n/2-1)!)+n!/2/(n/2)^2,Binomial[n,Ceiling[n/2]]Floor[n/2]!^2]; Table[f[n],{n,1,25}]
%Y A229244 Cf. A110468.
%K A229244 nonn
%O A229244 1,3
%A A229244 _Geoffrey Critzer_, Sep 17 2013