## Catalan numberAny number, u, from the Catalan sequence defined by_{n}u = (2_{n}n)! / (n + 1)!n!
It begins: 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, ... The values of u represent the number of
ways a polygon with _{n}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. ## Related categories• COMBINATORICS• TYPES OF NUMBERS | |||||

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