In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan (1814–1894)
The number of valid parenthesis expressions that consist of n right parentheses and left parentheses is equal to the nth Catalan number.
The first Catalan numbers for n = 0, 1, 2, 3, ... are
1, 1, 2, 5, 14, 42, 132, 429