A325956 Number of cyclic permutations of [n] with symmetry order s=1.

1, 0, 0, 4, 20, 108, 714, 4992, 40284, 362480, 3628790, 39912648, 479001588, 6226974684, 87178287120, 1307673722880, 20922789887984, 355687417715904, 6402373705727982, 121645100223034480, 2432902008175589664, 51090942167993548700, 1124000727777607679978, 25852016738803204991232

Offset: 1

Author

Michel Marcus, Sep 10 2019

Keywords

• nonn

Links

• Saeed Zakeri, Cyclic Permutations: Degrees and Combinatorial Types, arXiv:1909.03300 [math.DS], 2019. See Table 1 p. 8.

Crossrefs

Cf. A002619, A064852.

Programs

Mathematica

Table[(1/n) DivisorSum[n, MoebiusMu[#] EulerPhi[#] #^(n/#)*(n/#)! &], {n, 24}] (* Michael De Vlieger, May 07 2021 *)

PARI

a(n) = sumdiv(n, d, moebius(d)*eulerphi(d)*d^(n/d)*(n/d)!)/n;

Formula

a(n) = (1/n)*Sum_{d|n} moebius(d)*phi(d)*d^(n/d)*(n/d)!.

a(n) = n*A064852(n). - Andrew Howroyd, May 07 2021

Extensions

a(1)=1 prepended by Andrew Howroyd, May 07 2021