Everything about Catalan Number totally explained
In
combinatorial mathematics, the
Catalan numbers form a
sequence of
natural numbers that occur in various
counting problems, often involving
recursively defined objects. They are named for the
Belgian mathematician Eugène Charles Catalan (1814–1894).
The
nth Catalan number is given directly in terms of
binomial coefficients by
» , or
. This is the solution to labelled variants of the above combinatorics problems. It is entirely distinct from the
multifactorials.
History
The Catalan sequence was first described in the
18th century by
Leonhard Euler, who was interested in the number of different ways of dividing a polygon into triangles. The sequence is named after
Eugène Charles Catalan, who discovered the connection to parenthesized expressions during his exploration of the
Towers of Hanoi puzzle. The counting trick for Dyck words was found by D. André in 1887.
Further Information
Get more info on 'Catalan Number'.
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