---
tag: 0YWZJEABB2
kind: concept
name: Catalan numbers
msc: [05A15]
sources:
  - url: https://en.wikipedia.org/wiki/Catalan_number
    locator: lead section
same_as:
  wikidata: Q270513
  wikipedia: Catalan number
---

## Summary

The Catalan numbers $C_n$ form a sequence that counts many recursive structures, such as Dyck words, binary trees and bracketings. They satisfy a convolution recurrence and the formula $C_n = \binom{2n}{n}/(n+1)$. The node [[Catalan numbers|092DRBFKMG]] gives the precise definition.