Número Catalan C_n
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Catalan number C_n calculator is a mathematical tool that computes the Catalan sequence, defined by the formula (2n)! / [(n+1)!n!]. This sequence arises in combinatorial problems such as counting valid parentheses, grid paths, or binary trees. To use it, simply input a positive integer n, and the calculator will return the corresponding number.
Catalan numbers grow exponentially, which can limit their computational feasibility for very large n. This tool is ideal for educational purposes or projects involving combinatorial counting, like algorithm analysis or graph theory. Avoid values of n above 100 to prevent computational overload.
Practical examples include analyzing well-formed mathematical expressions, counting network paths, or even calculations in genetics. The formula, though simple, is foundational in discrete mathematics and has applications in computer science, statistics, and engineering.
Frequently asked questions
What is the Catalan sequence used for?
It solves combinatorial problems like counting valid parentheses, binary trees, or grid paths, with applications in discrete math and computer science.
Does the calculator work with fractional n values?
No, the formula requires a positive integer n. Fractional or negative values are invalid in the Catalan sequence.
Is there an alternative recursive formula?
Yes, C_n = Σ_{i=0}^{n-1} C_i * C_{n-i-1}, but this tool uses the direct factorial formula for computational efficiency.
What are practical usage limits?
Values above n=20 produce extremely large numbers. We recommend limiting to n ≤ 50 to avoid precision loss.