cp's OEIS Frontend

A155519 a(n) = Sum (J(p): p is a permutation of {1,2,...,n}), where J(p) is the number of j <= ceiling(n/2) such that p(j) + p(n+1-j) = n+1.

%I A155519 #7 Jul 21 2017 10:44:43
%S A155519 1,2,4,16,72,432,2880,23040,201600,2016000,21772800,261273600,
%T A155519 3353011200,46942156800,697426329600,11158821273600,188305108992000,
%U A155519 3389491961856000,64023737057280000,1280474741145600000
%N A155519 a(n) = Sum (J(p): p is a permutation of {1,2,...,n}), where J(p) is the number of j <= ceiling(n/2) such that p(j) + p(n+1-j) = n+1.
%C A155519 a(n) = Sum_{k=0..ceiling(n/2)} k*A155517(n,k).
%F A155519 a(2n-1) = n(2n-2)!; a(2n) = 2(2n-2)!*n^2.
%e A155519 a(3)=4 because J(123)=2 (counting j=1,2), J(321)=2 (counting j=1,2) and J(132) = J(312) = J(213) = J(231) = 0.
%p A155519 a := proc (n) if `mod`(n, 2) = 1 then (1/2)*(n+1)*factorial(n-1) else (1/2)*factorial(n-2)*n^2 end if end proc: seq(a(n), n = 1 .. 23);
%Y A155519 Cf. A155517, A155518.
%K A155519 nonn
%O A155519 1,2
%A A155519 _Emeric Deutsch_, Jan 26 2009