numbers (version 0.7-5)

catalan: Catalan Numbers

Description

Generate Catalan numbers.

Usage

catalan(n)

Arguments

n

integer, asking for the n-th Catalan number.

Value

A single integer, as long as n<=30.

Details

Catalan numbers, commonly denoted as \(C_n\), are defined as $$C_n = \frac{1}{n+1} {2 n \choose n}$$ and occur regularly in all kinds of enumeration problems.

Examples

# NOT RUN {
C <- numeric(10)
for (i in 1:10) C[i] <- catalan(i)
C[5]                                #=> 42
# }