### Catalan Numbers CalculatorWith Arbitrary Precision Arithmetic

Doing Math with JavaScript
 Input n (up to 25000):` ` Result: the Catalan number C(n)   (to select: click, Ctrl+A, Ctrl+C) Run time: n = n = n = n = n =

The Catalan numbers C(n) can be defined in several equivalent ways. A formal definition is:

C(n) = (2n)!/(n!(n+1)!).

Another definition: C(n) is the number of ways to insert n pairs of parentheses in an expression with n+1 terms. For example, if n = 2 there are two ways: `((ab)c)` or `(a(bc))`; if n = 3 there are 5 ways: `((ab)(cd))`, `(((ab)c)d)`, `((a(bc))d)`, `(a((bc)d))`, `(a(b(cd)))`. Accordingly, C(2) = 2 and C(3) = 5.

The Catalan sequence is OEIS A000108; in the Online Encyclopedia of Integer Sequences you can find lots of additional information and further references on Catalan numbers.

This online calculator computes the Catalan numbers C(n) for input values 0 ≤ n ≤ 25000 in arbitrary precision arithmetic. So, for example, you will get all 598 digits of C(1000) – a very large number!