A374262 Number of permutations of [n] such that the number of cycles of length k is a multiple of k for every k.

1, 1, 1, 1, 4, 16, 46, 106, 316, 3564, 27756, 141516, 556656, 6678816, 73015944, 521124696, 6144018336, 75200767776, 677927254176, 4642387894944, 75217104395136, 1167068528384256, 12348761954020416, 97377968145352896, 882819252604721664, 66882151986021043200

Offset: 0

Author

Alois P. Heinz, Jul 01 2024

Keywords

• nonn

Examples

			a(4) = 4: (1)(2)(3)(4), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..470
• Wikipedia, Permutation

Crossrefs

Cf. A000704, A130268, A372545, A372579, A374292, A374320.

Programs

Maple

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