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A111276
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Number of chiral non-crossing partition patterns of n points on a circle, divided by 2.
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0
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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
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1,6
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COMMENTS
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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.
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LINKS
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FORMULA
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MATHEMATICA
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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];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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