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

0,5

Links

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

Wikipedia, Permutation

Example

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).

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<n, 0,
       `if`(n=0, p!*f(m-p), b(n, i-1, p)+b(n-i, min(n-i, i-1), p-1)))
      end: b(m$3)
    end:
seq(a(n), n=0..24);

Crossrefs

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

Sequence in context: A357661 A371399 A061834 * A360590 A362244 A362238

Adjacent sequences: A364280 A364281 A364282 * A364284 A364285 A364286

Keyword

nonn

Author

Alois P. Heinz, Jul 17 2023

Status

approved