Don't touch me

The points \(1,2,\ldots, 9\) are labelled clockwise around a circle. How many ways can a subset of the chords be drawn between these points so that no pair of chords intersects?

Details and assumptions

Chords are not allowed to intersect at vertices nor at interior points.

It is implicit in the question that since an odd number of points are given, not all the points will correspond to a chord.

The empty set of chords satisfies the above conditions.


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