A323807 Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = floor(n/2).

1, 1, 2, 9, 23, 157, 503, 4833, 18827, 234061, 1076807, 16447329, 87358763, 1583571277, 9541763303, 200258110593, 1350025656107, 32202026068621, 240183024181127, 6418149695049249, 52479230675397803, 1553052337531253197, 13814973114258788903, 448537638127408597953, 4312466658317635366187

Offset

1,3

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = A130152(n,floor(n/2)).

Example

a(4) = 9: 1342, 1423, 1432, 2314, 2413, 3124, 3142, 3214, 3412.
a(5) = 23: 12453, 12534, 12543, 13425, 13524, 14235, 14253, 14325, 14523, 21453, 21534, 21543, 23145, 23154, 24135, 24153, 31245, 31254, 31425, 31524, 32145, 32154, 34125.

Crossrefs

Cf. A130152.

Sequence in context: A349189 A091107 A133469 * A075714 A101583 A339923

Adjacent sequences: A323804 A323805 A323806 * A323808 A323809 A323810

Keyword

nonn

Author

Alois P. Heinz, Jan 28 2019

Status

approved