Nº Catalan n

The Catalan number n calculator computes the n-th Catalan number, a sequence of natural numbers that appears in many combinatorial problems. The Catalan number is defined by the formula C_n = C(2n,n)/(n+1), where C(2n,n) is the binomial coefficient. This calculator allows you to input a non-negative integer n and obtain the corresponding Catalan number quickly and accurately.

The calculation is based on the closed-form formula for Catalan numbers. Internally, the calculator computes the binomial coefficient C(2n,n) and divides by (n+1). For large n, Catalan numbers grow rapidly, so the calculator may return results in scientific notation or limit precision as needed. It is important that n is a non-negative integer, as the sequence is defined for these values.

You can use this calculator in combinatorial problems, such as counting the number of ways to form balanced parentheses, paths in a grid that do not cross the diagonal, or complete binary trees. For example, C_3 = 5, which corresponds to the number of ways to combine 3 pairs of parentheses correctly. It is useful for mathematics students, programmers, and combinatorics enthusiasts.

Be careful when entering very large n, as Catalan numbers grow exponentially. The calculator may not be able to represent the exact result for n above 30 or 40, depending on the environment. Also, ensure that n is an integer and non-negative; fractional or negative values do not make sense for the Catalan sequence.