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