A075866 Number of permutations s of {1,2,...,n} such that |s(i)-i| for i=1,2,...,n are all distinct.

1, 1, 0, 0, 4, 4, 0, 0, 32, 96, 0, 0, 992, 2512, 0, 0, 50512, 144144, 0, 0, 3717888, 11068560, 0, 0, 378849504, 1269763552, 0, 0, 51487458416, 181839037824, 0, 0

Offset: 0

Author

Reiner Martin, Oct 15 2002

Keywords

• more
• nonn

Comments

a(n) = 0 iff n == 2,3 (mod 4).

Examples

			a(8) = 32, since the following 32 permutations of {12345678} and no others, have the required property:
  (87265314)(87361542)(87362514)(87364215)(87514632)(87531642)(87532614)
  (87541362)(83765142)(85724613)(84752613)(85743162)(86275413)(86374152)
  (86357142)(86542713)(48753621)(68275431)(68374251)(58376421)(58473621)
  (68357241)(68542731)(58643721)(73865241)(75824631)(74852631)(75843261)
  (73685421)(75386421)(75483621)(76358421).
		

Links

• H. A. Shah Ali, Problem 10964, Amer. Math. Monthly, 109 (2002), 759.

Crossrefs

Cf. A125183.

Formula

a(n) = A125183(n,n). - Alois P. Heinz, Feb 16 2019

Extensions

Extended and edited by John W. Layman, Oct 05 2004

a(17)-a(27) from Al Zimmermann, Aug 03 2007

a(28) through a(31) from Al Zimmermann, Aug 22 2007

a(0)=1 prepended by Alois P. Heinz, Feb 16 2019