Catalan number

Named after the Belgian mathematician Eugène Catalan (1814–1894).

Catalan number (plural Catalan numbers)

1. In combinatorial mathematics, any of a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects; the n^th Catalan number is equal to (2n choose n) over (n+1).
   • 1998 July 29, Michael Collins, “A CONTEXT-FREE GRAMMAR FOR ENGLISH”, in http://old-site.clsp.jhu.edu/ws98/projects/nlp/‎, retrieved 2013-04-19:

     AMBIGUITY LEADS TO AN EXPONENTIAL NUMBER OF TREES
     I saw the man with the telescope on the box in the car under the table ...
     n prepositional phrases ⇒ (n + 1)’th catalan number

   C_n — the n^th Catalan number — could be described as the number of distinct ways in which a sequence of n + 1 numbers could be associated by means of some specified binary operator.