Catalan sequence
The Catalan sequence is a sequence of positive integers that arise as the solution to a wide variety of combinatorial problems. The first few terms of the Catalan sequence are , , , , .... In general, the th term of the Catalan sequence is given by the formula , where is the th central binomial coefficient.
Introduction
The Catalan sequence can be used to find:
- The number of ways to arrange pairs of matching parentheses.
- The number of ways a convex polygon of sides can be split into triangles by nonintersection diagonals.
- The number of rooted binary trees with exactly leaves.
Example
In how many ways can the product of ordered number be calculated by pairs? For example, the possible ways for are and .