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A333804 (1/16) times the number of permutations p of [n+2] such that |p(i+n) - p(i)| <> n for i in {1,2}.

%I A333804 #11 Jun 28 2020 08:37:02
%S A333804 0,0,1,5,34,258,2172,20220,207000,2315880,28143360,369411840,
%T A333804 5210956800,78636096000,1264324723200,21579740582400,389730550809600,
%U A333804 7425628898688000,148865650053120000,3132539179241472000,69036795668865024000,1590266397644660736000
%N A333804 (1/16) times the number of permutations p of [n+2] such that |p(i+n) - p(i)| <> n for i in {1,2}.
%H A333804 Alois P. Heinz, <a href="/A333804/b333804.txt">Table of n, a(n) for n = 0..448</a>
%H A333804 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A333804 E.g.f.: 1/(2*x-2)-1/(8*(x-1)^3)+log(1-x)*(1-x)/2+(5*x+3)/8.
%F A333804 a(n) = A333706(n+2,n)/16.
%e A333804 a(2) = 1: there are 16 permutations p of [4] such that |p(i+2) - p(i)| <> 2 for i in {1,2}: 1243, 1324, 1342, 1423, 2134, 2314, 2413, 2431, 3124, 3142, 3241, 3421, 4132, 4213, 4231, 4312.
%p A333804 a:= proc(n) option remember; `if`(n<3, (n-1)*n/2, a(n-1)*
%p A333804      (n-2)*(n^4+2*n^3-9*n^2+6*n+8)/(n^4-2*n^3-9*n^2+26*n-8))
%p A333804     end:
%p A333804 seq(a(n), n=0..23);
%Y A333804 Cf. A333706.
%K A333804 nonn
%O A333804 0,4
%A A333804 _Alois P. Heinz_, Apr 05 2020