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%I #15 Jul 02 2018 10:07:24
%S 1,1,2,2,4,5,12,19,46,95,230,528,1320,3219,8172,20714,53478,138635,
%T 363486,957858,2543476,6788019,18218772,49120019,133036406,361736109,
%U 987316658,2703991820,7429445752,20473889133,56579632732,156766505691
%N Unlabeled (cyclic) Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n unlabeled points equally spaced on a circle, up to rotations of the circle.
%C Unlabeled version of A001006.
%C The number of such chord configurations on 2n vertices with n chords is given by A002995(n+1).
%H Andrew Howroyd, <a href="/A175954/b175954.txt">Table of n, a(n) for n = 0..200</a>
%H Andrew Howroyd, <a href="/A175954/a175954.txt">Chord Configuration Symmetries</a>
%F For odd prime p, a(p) = (A001006(p) - 1)/p + 1.
%F a(n) = (1/n) * (A001006(n) + A142150(n) * A001006(n/2-1) + Sum{d|n, d<n} totient(n/d) * A002426(d)). - _Andrew Howroyd_, Apr 01 2017
%t a1006[0] = 1; a1006[n_Integer] := a1006[n] = a1006[n-1] + Sum[a1006[k]* a1006[n -2-k], {k, 0, n-2}];
%t a142150[n_] := n*(1 + (-1)^n)/4;
%t a2426[n_] := Coefficient[(1 + x + x^2)^n, x, n];
%t a[0] = 1; a[n_] := (1/n)*(a1006[n]+a142150[n]*a1006[n/2-1] + Sum[EulerPhi[ n/d]*a2426[d], {d, Most @ Divisors[n]}]);
%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Jul 02 2018, after _Andrew Howroyd_ *)
%Y Cf. A001006, A185100, A002426, A002995.
%K nonn
%O 0,3
%A _Max Alekseyev_, Oct 29 2010
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