CatalanNumber
gives the n Catalan number
.
Details

- CatalanNumber[n] is generically defined as
.
- Catalan numbers are integers for integer arguments, and appear in various tree enumeration problems.
- CatalanNumber can be used with Interval and CenteredInterval objects: »
Examples
open allclose allScope (8)
Evaluate for half-integer arguments:
Evaluate for complex arguments:
Compute sums involving CatalanNumber:
CatalanNumber threads element-wise over lists:
CatalanNumber can be used with Interval and CenteredInterval objects:
TraditionalForm typesetting:
Applications (1)
Compute the number of different ways to parenthesize an expression:
Distribute over lists in CirclePlus:
Use the pattern matcher to repeatedly split the list into two parts in all possible ways:
Properties & Relations (5)
The generating function for Catalan numbers:
Catalan numbers can be represented as difference of binomial coefficients:
CatalanNumber can be represented as a DifferenceRoot:
FindSequenceFunction can recognize the CatalanNumber sequence:
The exponential generating function for CatalanNumber:
Possible Issues (1)
Neat Examples (2)
The only odd Catalan numbers are those of the form CatalanNumber[2k-1]:
Determinants of Hankel matrices made out of Catalan numbers:
Text
Wolfram Research (2007), CatalanNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/CatalanNumber.html (updated 2014).
CMS
Wolfram Language. 2007. "CatalanNumber." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/CatalanNumber.html.
APA
Wolfram Language. (2007). CatalanNumber. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CatalanNumber.html