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.
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