A364281 Number of permutations of [n] with distinct cycle lengths such that each cycle contains exactly one cycle length as an element.

1, 1, 1, 4, 10, 48, 252, 1584, 10800, 93600, 823680, 8588160, 93381120, 1158312960, 14805504000, 215028172800, 3159494553600, 51973589606400, 873152856576000, 16058241239040000, 300754643245056000, 6159522883497984000, 127439374149255168000

Offset

0,4

Links

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

Wikipedia, Permutation

Example

a(3) = 4: (123), (132), (13)(2), (1)(23).
a(4) = 10: (1234), (1243), (1324), (1342), (1423), (1432), (124)(3),
   (142)(3), (1)(234), (1)(243).

Maple

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!*(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);

Mathematica

a[m_] := a[m] = Module[{b}, b[n_, i_, p_] := b[n, i, p] = If[i(i+1)/2 < n, 0, If[n == 0, p!*(m - p)!, b[n, i - 1, p] + b[n - i, Min[n - i, i - 1], p - 1]]]; b[m, m, m]];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Oct 21 2023, after Alois P. Heinz *)

Crossrefs

Cf. A327712, A364279, A364406.

Sequence in context: A099606 A149231 A335873 * A173086 A081565 A151611

Adjacent sequences: A364278 A364279 A364280 * A364282 A364283 A364284

Keyword

nonn

Author

Alois P. Heinz, Jul 17 2023

Status

approved