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

0,5

Comments

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

Links

Table of n, a(n) for n=0..31.

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

Formula

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

Example

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).

Crossrefs

Cf. A125183.

Sequence in context: A282593 A276339 A260318 * A202168 A156450 A067007

Adjacent sequences: A075863 A075864 A075865 * A075867 A075868 A075869

Keyword

more,nonn

Author

Reiner Martin, Oct 15 2002

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

Status

approved