%I #19 Aug 28 2019 08:15:05

%S 1,1,1,2,6,15,46,132,432,1384,4735,16158,56766,200473,718012,2587000,

%T 9398080,34324173,126067124,465093570,1723171550,6407924165,

%U 23910560070,89494164972,335913861648,1264107416450,4768452532025

%N Number of 2n-bead black-white reversible necklaces with n black beads and fundamental period 2n.

%H Andrew Howroyd, <a href="/A045628/b045628.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Br#bracelets">Index entries for sequences related to bracelets</a>

%F Moebius transform of A005648. - _Christian G. Bower_

%F a(n) = 1/(4*n) * Sum_{d|n} mu(n/d) * (2*n*binomial(2*floor(d/2), floor(d/2)) + binomial(2*d, d)) for n > 0. - _Andrew Howroyd_, Sep 28 2017

%t a[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] (2n Binomial[ 2 Quotient[d, 2], Quotient[d, 2]] + Binomial[2d, d]), {d, Divisors[n]}]/(4n)];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Aug 28 2019, from PARI *)

%o (PARI) a(n) = if(n<1, n==0, sumdiv(n,d, moebius(n/d)*(2*n*binomial(2*(d\2), d\2) + binomial(2*d, d)))/(4*n)); \\ _Andrew Howroyd_, Sep 28 2017

%Y Cf. A005648.

%K nonn

%O 0,4

%A _David W. Wilson_