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

Author

Darío Clavijo, May 11 2025

Keywords

• nonn
• easy

Examples

			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.

Formula

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