A155518 Number of permutations p of {1,2,...,n} such that p(j) + p(n+1-j) != n+1 for all j.

1, 0, 0, 4, 16, 64, 384, 2880, 23040, 208896, 2088960, 23193600, 278323200, 3640688640, 50969640960, 768126320640, 12290021130240, 209688566169600, 3774394191052800, 71921062285148160, 1438421245702963200

Offset: 0

Author

Emeric Deutsch, Jan 26 2009

Keywords

• nonn

Examples

			a(3)=4 because we have 132, 312, 213 and 231 (123 and 321 do not qualify).
		

Crossrefs

Cf. A053871, A155517, A155519.

Programs

Maple

g[0] := 1: g[1] := 0: for n from 2 to 20 do g[n] := (2*(n-1))*(g[n-1]+g[n-2]) end do: a := proc (n) if `mod`(n, 2) = 1 then factorial((1/2)*n-1/2)*2^((1/2)*n-1/2)*g[(1/2)*n+1/2] else factorial((1/2)*n)*2^((1/2)*n)*g[(1/2)*n] end if end proc: seq(a(n), n = 0 .. 24);

Formula

a(n) = A155517(n,0).

a(2n-1) = (n-1)!*2^(n-1)*g(n), a(2n) = n!*2^n*g(n), where g(n) = A053871(n) is defined by g(0)=1, g(1)=0, g(n) = 2(n-1)*(g(n-1) + g(n-2)) for n>=2.