A364283 Number of permutations of [n] with distinct cycle lengths such that each cycle contains exactly one cycle length different from its own as an element.

1, 0, 0, 1, 2, 12, 60, 408, 2640, 24480, 208080, 2262960, 23950080, 307359360, 3835641600, 57400358400, 825160089600, 13909727462400, 229664981145600, 4310966499840000, 79428141112320000, 1658163790483200000, 33795850208440320000, 770528520983789568000

Offset: 0

Author

Alois P. Heinz, Jul 17 2023

Keywords

• nonn

Examples

			a(3) = 1: (13)(2).
a(4) = 2: (124)(3), (142)(3).
a(5) = 12: (1235)(4), (1253)(4), (1325)(4), (1352)(4), (1523)(4), (1532)(4),
   (124)(35), (142)(35), (125)(34), (152)(34), (13)(245), (13)(254).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450
• Wikipedia, Permutation

Crossrefs

Cf. A000009, A000166, A007838, A362362, A364277, A364279, A364281, A364282, A364406.

Programs

Maple

f:= proc(n) option remember; `if`(n<2, 1-n, (n-1)*(f(n-1)+f(n-2))) end:
a:= proc(m) option remember; local b; b:=
      proc(n, i, p) option remember; `if`(i*(i+1)/2