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Catalan number

Any number, un, from the Catalan sequence defined by

un = (2n)! / (n + 1)!n!

It begins: 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, ... The values of un represent the number of ways a polygon with n + 2 sides can be cut into n triangles using straight lines joining vertices and are named after the Belgian mathematician Eugène Catalan (1814-1894). They also arise in other counting problems, for example in determining how many ways 2n beans can be divided into two containers if one container can never have less than the second.

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