OFFSET
1,6
COMMENTS
Half of the number of those rotation-inequivalent patterns of non-crossing partitions of n (equally spaced) points on a circle which are not invariant under reflections. Division by two counts one pattern from each chiral (Right-handed,Left-handed) pair.
LINKS
D. Callan and L. Smiley, Non-crossing Partitions under Rotation and Reflection, arXiv:math/0510447 [math.CO], 2005.
L. Smiley, a(5) = 0
L. Smiley, a(6)=8/2=4
MATHEMATICA
a[n_] := If[n < 6, 0, ((Binomial[2n, n]/(n+1) + DivisorSum[n, Binomial[2#, #] EulerPhi[n/#] Boole[# < n]&])/n - Binomial[n, Floor[n/2]])/2];
Array[a, 22] (* Jean-François Alcover, Feb 17 2019 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
David Callan and Len Smiley, Oct 21 2005
STATUS
approved