OldJavaGeek

Catalan numbers are a sequence of natural numbers that appear in various combinatorial problems, often related to recursively defined structures. These numbers are widely used in counting problems, particularly in dynamic programming and combinatorics. The sequence of Catalan numbers starts as follows: C 0 = 1 , C 1 = 1 , C 2 = 2 , C 3 = 5 , C 4 = 14 , C 5 = 42 , … C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, C_5 = 42, \dots Formula for Catalan Numbers The n-th Catalan number can be computed using the following formula: C n = ∑ i = 0 n − 1 C i ⋅ C n − i − 1 C_n = \sum_{i=0}^{n-1} C_i \cdot C_{n-i-1} Alternatively, it can be expressed using the binomial coefficient: Catalan numbers are a sequence of natural numbers that appear in various combinatorial problems, often related to recursively defined structures. These numbers are widely used in counting problems, particularly in dynamic programming and combinatorics. The sequence of Catalan numbers starts as follows: Formula for Catalan ...