> For the complete documentation index, see [llms.txt](https://trizen.gitbook.io/sidef-lang/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://trizen.gitbook.io/sidef-lang/programming_tasks/c/catalan_numbers.md).

# Catalan numbers

```ruby
func f(i) { i==0 ? 1 : (i * f(i-1)) }
func c(n) { f(2*n) / f(n) / f(n+1) }
```

With memoization:

```ruby
func c(n) is cached {
    n == 0 ? 1 : (c(n-1) * (4 * n - 2) / (n + 1))
}
```

Calling the function:

```ruby
15.times { |i|
    say "#{i}\t#{c(i)}"
}
```

#### Output:

```
0       1
1       1
2       2
3       5
4       14
5       42
6       132
7       429
8       1430
9       4862
10      16796
11      58786
12      208012
13      742900
14      2674440
```