Problem 42821. Polygon division

Given the number of vertices (or sides), n, of a planar convex polygon, return the number of ways, w, in which you can divide the polygon into triangles, such that:

1. The division is done by drawing straight lines between existing vertices.

2. The triangles are made of existing vertices.

3. Different orientations of a similar solution are counted as different solutions.

Assume that n is a positive integer greater than 2.

Example 1:

n = 4 (square)

w = 2 (you can draw a line between vertices 1 and 3, as well as a line between vertices 2 and 4)

Example 2:

n = 5 (pentagon)

w = 5