The Catalan numbers are a sequence of natural numbers, one, one, two, five, fourteen, forty-two and so on, that count an unusually wide range of recursively structured objects: the ways to correctly match n pairs of parentheses, the distinct binary trees with n internal nodes, and the ways to divide a convex polygon with n plus two sides into triangles, among many others. The nth Catalan number is given by one over n plus one, multiplied by the binomial coefficient of two n choose n. They are named after the Belgian mathematician Eugene Charles Catalan, although the Mongolian mathematician Mingantu had already found the same sequence in the 1730s, decades earlier.
Facts
Partially Attested
Origin YearFirst described in Western mathematical literature by Euler in 1751; the entity's existing description notes the Mongolian mathematician Mingantu's independent, earlier but less precisely dated work, from the 1730s. Sources
1. Catalan Number (Wikipedia)
History sectionQuote, History section
The Catalan sequence was described in 1751 by Leonhard Euler, who was interested in the number of different ways of dividing a polygon into triangles.
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