A369074 Number of permutations of [n] such that for each cycle the arithmetic mean of the elements is an integer.

1, 1, 1, 4, 8, 50, 144, 1416, 4956, 73776, 257040, 5945376, 27326592, 741487104, 2932516224, 131001886656, 638526753792, 29531870206848, 134850149263872, 8724620122025472, 44681558679940608, 3278334059973665280, 14043776731843497984, 1454550035837209454592

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Wikipedia, Permutation

Example

a(0) = 1: the empty permutation.
a(1) = 1: (1).
a(2) = 1: (1)(2).
a(3) = 4: (123), (132), (13)(2), (1)(2)(3).
a(4) = 8: (123)(4), (132)(4), (13)(24), (13)(2)(4), (1)(234), (1)(243),
  (1)(24)(3), (1)(2)(3)(4).

Crossrefs

Cf. A000142, A327475, A369073.

Sequence in context: A056407 A329942 A056397 * A189314 A358791 A215746

Adjacent sequences: A369071 A369072 A369073 * A369075 A369076 A369077

Keyword

nonn

Author

Alois P. Heinz, Jan 12 2024

Extensions

a(18)-a(23) from Christian Sievers, Nov 22 2024

Status

approved