Catalan number

noun

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).

“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.”

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

nounCatalan number (plural Catalan numbers)

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 nᵗʰ Catalan number is equal to (2n choose n) over (n+1).

    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.

    1 more example

    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

    1998 July 29, Michael Collins, “A CONTEXT-FREE GRAMMAR FOR ENGLISH”, in http://old-site.clsp.jhu.edu/ws98/projects/nlp/, retrieved 19 Apr 2013

Origin

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

Full word history & related roots →
Cite this entry
APA

Catalan number. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Catalan%20number

MLA

“Catalan number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Catalan%20number. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Catalan number,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Catalan%20number.

Source: Catalan number on Wiktionary, CC BY-SA 4.0.