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

0,4

Links

Table of n, a(n) for n=0..20.

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.

Example

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

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);

Crossrefs

Cf. A053871, A155517, A155519.

Sequence in context: A097679 A158778 A227313 * A005401 A002923 A345365

Adjacent sequences: A155515 A155516 A155517 * A155519 A155520 A155521

Keyword

nonn

Author

Emeric Deutsch, Jan 26 2009

Status

approved