Sets of Non-Self-Intersecting Paths Connecting the Vertices of a Convex Polygon

The paper deals with counting the sets of non-self-intersecting paths whose nodes form a partitioning of the set of vertices of a given convex polygon. There turn to exist compact formulae when the magnitude of these sets is fixed. Some of these formulae provide new properties for some of the entries of the On-line Encyclopedia of Integer Sequences, while others generate new entries therein.