A383835 Number of permutations of [n] whose compositional square is the identity permutation or its reverse.

1, 1, 2, 4, 12, 28, 76, 232, 776, 2632, 9496, 35696, 140272, 568624, 2390480, 10349536, 46208416, 211800992, 997313824, 4809701440, 23758694336, 119952723136, 618884638912, 3257843882624, 17492191242880, 95680444425856, 532985208200576, 3020676745975552

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = A000085(n) + A037224(n) for n > 1.

Example

a(4) = A000085(4) + A037224(4) = 10 + 2 = 12: 1234, 1243, 1324, 1432, 2134, 2143, 3214, 3412, 4231, 4321, 2413, 3142.

Crossrefs

Cf. A000085, A000142, A037224.

Sequence in context: A096581 A275434 A364316 * A381123 A151258 A148175

Adjacent sequences: A383832 A383833 A383834 * A383836 A383837 A383838

Keyword

nonn,easy

Author

Darío Clavijo, May 11 2025

Status

approved