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

Author

Gary Yane, Apr 20 2021

Keywords

• nonn
• easy

Examples

			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).
		

Links

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

Crossrefs

Cf. A000040, A001358, A005225, A261431.

Programs

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

PARI

a(n) = if (n, sumdiv(n, d, if (dMichel Marcus, Apr 21 2021

Formula

a(n) = Sum_{d|n, d0, a(0) = 1.

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