A321520 -id:A321520 - cp's OEIS frontend

A362362 Number of permutations of [n] such that each cycle contains its length as an element.

1, 1, 1, 3, 8, 36, 174, 1104, 7440, 62640, 545040, 5649840, 60681600, 748621440, 9518342400, 136758585600, 2009451628800, 32848492723200, 549241915622400, 10066913176320000, 188293339922688000, 3832031198451456000, 79291640831090688000, 1771146970953744384000

Offset: 0

Alois P. Heinz, Jul 05 2023

nonn

The cycle lengths are distinct as a consequence of the definition.

			a(3) = 3: (123), (132), (1)(23).
a(4) = 8: (1234), (1243), (1324), (1342), (1423), (1432), (1)(234), (1)(243).

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

Cf. A000009, A007838, A032020, A179973, A321520, A326493, A364277, A364406.

a:= n-> add((n-nops(p))!, p=select(l-> nops(l)=
        nops({l[]}), combinat[partition](n))):
seq(a(n), n=0..24);
# second Maple program:
b:= proc(n, i, p) option remember; `if`(i*(i+1)/2 b(n$3):
seq(a(n), n=0..24);

b[n_, i_, p_] := b[n, i, p] = If[i*(i + 1)/2 < n, 0, If[n == 0, p!, b[n, i - 1, p] + b[n - i, Min[n - i, i - 1], p - 1]]];
a[n_] := b[n, n, n];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Nov 15 2023, from second Maple program *)

cp's OEIS Frontend

A362362 Number of permutations of [n] such that each cycle contains its length as an element.

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