Catalan Number

The Catalan numbers are a sequence of natural numbers that occur in many counting problems, often ones involving recursively defined objects, and are named after Eugene Catalan even though they were first discovered in the 1730s by the Mongolian mathematician Minggatu. The n-th Catalan number can be written directly in terms of a central binomial coefficient, as the quantity (2n) factorial divided by (n plus 1) factorial times n factorial, and the sequence begins 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862 and upward for n equal to 0, 1, 2, 3 and on. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/