K-angulation

A (k_1, k_2)-angulation of a convex $N$-gon is defined as a way to divide it into smaller polygons using diagonals that do not intersect each other, except at their endpoints. Each resulting polygon must have at least k_1 vertices and at most k_2 vertices.

Your task is to determine the number of distinct (k_1, k_2)-angulations of a convex $N$-gon. Two angulations are considered different if there is at least one diagonal present in one angulation that is not present in the other.