In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Catalan, though they were previously discovered in the 1730s by Minggatu.
The n-th Catalan number can be expressed directly in terms of the central binomial coefficients by
The first Catalan numbers for n = 0, 1, 2, 3, ... are