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In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles Catalan, though they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients by
  - C n = 1 n + 1 =!! n! = ∏ k = 2 n n + k k for  n ≥ 0. The first Catalan numbers for n = 0, 1, 2, 3,... are
  - 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786,....