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

0,5

Links

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

Wikipedia, Permutation

Example

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

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);

Crossrefs

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

Sequence in context: A379464 A000704 A374320 * A007315 A055342 A213292

Adjacent sequences: A374259 A374260 A374261 * A374263 A374264 A374265

Keyword

nonn

Author

Alois P. Heinz, Jul 01 2024

Status

approved