Catalan Numbers are a sequence of natural numbers that have many applications in combinatorial mathematics. They can be defined using a specific formula: C(n) = (2n)! / ((n + 1)!n!), where n is a non-negative integer. The first few Catalan numbers are 1, 1, 2, 5, 14, and 42. These numbers count various combinatorial structures, such as the number of ways to correctly match parentheses, the number of rooted binary trees with n nodes, and the number of paths along the edges of a grid that do not cross above a diagonal line.