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

%I A254083 #9 Feb 26 2017 10:54:27
%S A254083 1,0,3,89,5100,510288,79419060,17758540440,5397245411040,
%T A254083 2140495978400640,1073686615986821760,664582969579045104000,
%U A254083 497566995304189636425600,443212653988584641970547200,463237380681508395317004249600,561422444732790213860667834854400
%N A254083 Number of primitive (=aperiodic) 2n-bead necklaces with colored beads of exactly n different colors.
%H A254083 Alois P. Heinz, <a href="/A254083/b254083.txt">Table of n, a(n) for n = 0..200</a>
%F A254083 a(n) = A254040(2*n,n).
%e A254083 a(2) = 3: 0001, 0011, 0111.
%p A254083 with(numtheory):
%p A254083 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A254083       add(mobius(n/d)*k^d, d=divisors(n))/n)
%p A254083     end:
%p A254083 a:= n-> add(b(2*n, n-j)*binomial(n, j)*(-1)^j, j=0..n):
%p A254083 seq(a(n), n=0..20);
%t A254083 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 A254083 Cf. A254040.
%K A254083 nonn
%O A254083 0,3
%A A254083 _Alois P. Heinz_, Jan 25 2015