A254083 - OEIS

%I #9 Feb 26 2017 10:54:27

%S 1,0,3,89,5100,510288,79419060,17758540440,5397245411040,

%T 2140495978400640,1073686615986821760,664582969579045104000,

%U 497566995304189636425600,443212653988584641970547200,463237380681508395317004249600,561422444732790213860667834854400

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

%H Alois P. Heinz, <a href="/A254083/b254083.txt">Table of n, a(n) for n = 0..200</a>

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

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

%p with(numtheory):

%p b:= proc(n, k) option remember; `if`(n=0, 1,

%p       add(mobius(n/d)*k^d, d=divisors(n))/n)

%p     end:

%p a:= n-> add(b(2*n, n-j)*binomial(n, j)*(-1)^j, j=0..n):

%p seq(a(n), n=0..20);

%t 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 *)

%Y Cf. A254040.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jan 25 2015