A374292 Number of permutations of [n] such that the number of cycles of length k is zero or a divisor of k for every k.

1, 1, 1, 5, 17, 89, 474, 3324, 28440, 253448, 2476700, 26876420, 328110540, 4207321260, 58468831680, 877439227560, 14214209548560, 239870470655760, 4285924637475600, 81381169697904720, 1636049164466934000, 34301061146870607600, 750389221227585139200

Offset: 0

Author

Alois P. Heinz, Jul 02 2024

Keywords

• nonn

Examples

			a(3) = 5: (1)(2,3), (1,2)(3), (1,3)(2), (1,2,3), (1,3,2).
		

Links

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

Crossrefs

Cf. A372545, A372579, A374262, A374319.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(`if`(j=0 or irem(i, j)=0, b(n-i*j, i-1)*(i-1)!^j/j!*
      combinat[multinomial](n, i$j, n-i*j), 0), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);