

A111276


Number of chiral noncrossing partition patterns of n points on a circle, divided by 2.


0



0, 0, 0, 0, 0, 4, 14, 60, 210, 728, 2442, 8252, 27716, 93924, 319964, 1098900, 3800928, 13244836, 46460738, 164015272, 582353976, 2078812492
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OFFSET

1,6


COMMENTS

Half of the number of those rotationinequivalent patterns of noncrossing partitions of n (equally spaced) points on a circle which are not invariant under reflections. Division by two counts one pattern from each chiral (Righthanded,Lefthanded) pair.


LINKS

Table of n, a(n) for n=1..22.
D. Callan and L. Smiley, Noncrossing Partitions under Rotation and Reflection, arXiv:math/0510447 [math.CO], 2005.
L. Smiley, a(5) = 0
L. Smiley, a(6)=8/2=4


FORMULA

a(n) = (A054357(n)  A001405(n))/2.


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] (* JeanFrançois Alcover, Feb 17 2019 *)


CROSSREFS

Cf. A001405, A054357, A111275.
Sequence in context: A149492 A307488 A241706 * A149493 A299926 A307399
Adjacent sequences: A111273 A111274 A111275 * A111277 A111278 A111279


KEYWORD

nonn,more


AUTHOR

David Callan and Len Smiley, Oct 21 2005


STATUS

approved



