# Definition:Catalan Number

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## Definition

The Catalan Numbers $C_n$ are a sequence of natural numbers defined by:

$C_n = \dfrac 1 {n + 1} \dbinom {2 n} n$

## Sequence of Catalan Numbers

The sequence of Catalan numbers begins:

$(1,) \, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, \ldots$

where the inclusion or not of the initial $1$ depends on whether $n$ starts from $0$ or $1$.

## Also known as

The Catalan numbers are also known as Segner numbers for Johann Andreas Segner.

## Source of Name

This entry was named for Eugène Charles Catalan.