Catalan number

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English

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Etymology

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

Noun

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Catalan number (plural Catalan numbers)

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Wikipedia
  1. In combinatorial mathematics, any of a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects; the nth 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/[1], 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
    Cn — the nth 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.