A254083 Number of primitive (=aperiodic) 2n-bead necklaces with colored beads of exactly n different colors.

1, 0, 3, 89, 5100, 510288, 79419060, 17758540440, 5397245411040, 2140495978400640, 1073686615986821760, 664582969579045104000, 497566995304189636425600, 443212653988584641970547200, 463237380681508395317004249600, 561422444732790213860667834854400

Offset: 0

Author

Alois P. Heinz, Jan 25 2015

Keywords

• nonn

Examples

			a(2) = 3: 0001, 0011, 0111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A254040.

Programs

Maple

with(numtheory):
b:= proc(n, k) option remember; `if`(n=0, 1,
      add(mobius(n/d)*k^d, d=divisors(n))/n)
    end:
a:= n-> add(b(2*n, n-j)*binomial(n, j)*(-1)^j, j=0..n):
seq(a(n), n=0..20);

Mathematica

b[n_, k_] := b[n, k] = If[n==0, 1, DivisorSum[n, MoebiusMu[n/#]*k^#&]/n]; a[n_] := Sum[b[2n, n-j]*Binomial[n, j]*(-1)^j, {j, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 26 2017, translated from Maple *)

Formula

a(n) = A254040(2*n,n).