Catalan Number Calculator

Summary

Enter n to compute the nth Catalan number and see a table of the first N values in the sequence.

How it works

1. Enter a value of n (0 through 30) in the input field.
2. The calculator applies the closed-form formula C(n) = (2n)! / ((n+1)! × n!).
3. The result for C(n) is displayed immediately.
4. A table below lists every Catalan number from C(0) up to C(n).
5. Use the Copy button to copy the current result to your clipboard.

Use cases

• Verify Catalan number values for combinatorics homework or research.
• Count the number of valid parenthesizations of n+1 factors.
• Find the number of distinct binary trees with n internal nodes.
• Enumerate monotonic lattice paths that stay below the diagonal.
• Cross-check results in computational geometry and graph theory problems.
• Explore the growth rate of the Catalan sequence.

Frequently Asked Questions