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.

1, 2, 4, 16, 72, 432, 2880, 23040, 201600, 2016000, 21772800, 261273600, 3353011200, 46942156800, 697426329600, 11158821273600, 188305108992000, 3389491961856000, 64023737057280000, 1280474741145600000

Offset: 1

Author

Emeric Deutsch, Jan 26 2009

Keywords

• nonn

Comments

a(n) = Sum_{k=0..ceiling(n/2)} k*A155517(n,k).

Examples

			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.
		

Crossrefs

Cf. A155517, A155518.

Programs

Maple

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);

Formula

a(2n-1) = n(2n-2)!; a(2n) = 2(2n-2)!*n^2.