Definition:Catalan Number

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.

Also see

• Results about Catalan numbers can be found here.

Source of Name

This entry was named for Eugène Charles Catalan.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $42$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $42$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Catalan numbers (E.C. Catalan, 1838)

• Weisstein, Eric W. "Catalan Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalanNumber.html