Catalan Number Calculator
Catalan Number Calculator
Catalan numbers show up in a remarkably wide range of counting problems — from the number of ways to correctly match pairs of parentheses, to the number of distinct binary trees, to the number of ways to slice a polygon into triangles. Enter a value of n, and this calculator computes the corresponding Catalan number using the formula Cₙ = C(2n,n)/(n+1). The sequence starts 1, 1, 2, 5, 14, 42, 132 and grows roughly fourfold with each step, making it one of the fastest-growing sequences in common combinatorics problems.
- Catalan numbers count a huge range of combinatorial structures, including the number of ways to correctly match n pairs of parentheses, the number of distinct binary trees with n nodes, and the number of ways to triangulate a polygon.
- The formula is Cₙ = C(2n,n)/(n+1), built from an ordinary binomial coefficient divided by n+1.
- The sequence starts 1, 1, 2, 5, 14, 42, 132… and grows roughly by a factor of 4 with each step, making it one of the fastest-growing common combinatorial sequences.
How do I calculate the nth Catalan number?
Use the formula Cₙ = C(2n,n)/(n+1), where C(2n,n) is the binomial coefficient "2n choose n."
What is the 5th Catalan number?
C(10,5)/6 = 252/6 = 42.
Catalan Number Calculator
Catalan numbers show up in a remarkably wide range of counting problems — from the number of ways to correctly match pairs of parentheses, to the number of distinct binary trees, to the number of ways to slice a polygon into triangles. Enter a value of n, and this calculator computes the corresponding Catalan number using the formula Cₙ = C(2n,n)/(n+1). The sequence starts 1, 1, 2, 5, 14, 42, 132 and grows roughly fourfold with each step, making it one of the fastest-growing sequences in common combinatorics problems.
- Catalan numbers count a huge range of combinatorial structures, including the number of ways to correctly match n pairs of parentheses, the number of distinct binary trees with n nodes, and the number of ways to triangulate a polygon.
- The formula is Cₙ = C(2n,n)/(n+1), built from an ordinary binomial coefficient divided by n+1.
- The sequence starts 1, 1, 2, 5, 14, 42, 132… and grows roughly by a factor of 4 with each step, making it one of the fastest-growing common combinatorial sequences.
How do I calculate the nth Catalan number?
Use the formula Cₙ = C(2n,n)/(n+1), where C(2n,n) is the binomial coefficient "2n choose n."
What is the 5th Catalan number?
C(10,5)/6 = 252/6 = 42.