A343576 Number of permutations of [n] without fixed points and all cycles equal length.

1, 0, 1, 2, 9, 24, 175, 720, 6405, 42560, 436401, 3628800, 48073795, 479001600, 7116730335, 88966701824, 1474541093025, 20922789888000, 400160588853025, 6402373705728000, 133991603578884051, 2457732174030848000, 55735573291977790575, 1124000727777607680000

Offset

0,4

Links

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

Formula

a(n) = Sum_{d|n, d<n} (n!/d!)*(d/n)^d for n>0, a(0) = 1.

a(n) = A261431(n) for n in { A000040, A001358 }.

Example

a(4) = 9: (1,2)(3,4), (1,3)(2,4), (1,4)(2,3), (2,3,4,1), (2,4,1,3), (3,1,4,2), (3,4,2,1), (4,1,2,3), (4,3,1,2).

Maple

a:= n-> `if`(n=0, 1, add(n!/d!*(d/n)^d, d=numtheory[divisors](n) minus {n})):
seq(a(n), n=0..23);  # Alois P. Heinz, Apr 20 2021

Prog

(PARI) a(n) = if (n, sumdiv(n, d, if (d<n, (n!/d!)*(d/n)^d)), 1); \\ Michel Marcus, Apr 21 2021

Crossrefs

Cf. A000040, A001358, A005225, A261431.

Sequence in context: A137852 A347106 A097346 * A261431 A360515 A226388

Adjacent sequences: A343573 A343574 A343575 * A343577 A343578 A343579

Keyword

nonn,easy

Author

Gary Yane, Apr 20 2021

Status

approved