Result
C(n)
=
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About Catalan Numbers
Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects.
The first few Catalan numbers are:
- C(0) = 1
- C(1) = 1
- C(2) = 2
- C(3) = 5
- C(4) = 14
Catalan numbers appear in many counting problems, including:
- Number of ways to properly parenthesize n pairs of parentheses
- Number of ways to triangulate a convex polygon with n+2 sides
- Number of binary trees with n nodes
- Number of paths on a grid that don't cross the diagonal
The formula for the nth Catalan number is:
\[C_n = \frac{1}{n+1}\binom{2n}{n}\]
Note: Catalan numbers grow exponentially. Our calculator can handle values up to n = 100.