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%I #10 Oct 10 2019 22:20:51
%S 1,0,1,1,3,3,12,24,103,387,1819,8933,48632,279484,1716523,11126025,
%T 76014437,544945399,4089010392,32025053060,261213946739,2214280580389,
%U 19471365925297,177319383231697,1669735890602062,16235408370162588,162796351456044465,1681427459283678177
%N Number of n-bead necklace structures with no adjacent elements having the same color.
%C Beads may be of any number of colors. Colors may be permuted without changing the necklace structure.
%C Equivalently, the number of set partitions of an n-set up to rotations where no block contains cyclically adjacent elements of the n-set.
%H Andrew Howroyd, <a href="/A328150/b328150.txt">Table of n, a(n) for n = 0..200</a>
%e a(6) = 12 because there are the following 12 necklace structures: ABABAB, ABABAC, ABABCD, ABACAD, ABACBC, ABACBD, ABACDC, ABACDE, ABCABC, ABCABD, ABCADE, ABCDEF.
%o (PARI) seq(n)={Vec(1 + intformal(sum(m=1, n, eulerphi(m) * subst(serlaplace(-1 + exp(-x + sumdiv(m, d, (exp(d*x + O(x*x^(n\m)))-1)/d))), x, x^m))/x))} \\ _Andrew Howroyd_, Oct 09 2019
%Y Row sums of A327396.
%Y Cf. A084423.
%K nonn
%O 0,5
%A _Andrew Howroyd_, Oct 05 2019
%E Terms a(16) and beyond from _Andrew Howroyd_, Oct 09 2019
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