High Quality Content by WIKIPEDIA articles! In combinatorics, the Narayana numbers N, form a triangle of natural numbers, called Narayana triangle, that occur in various counting problems. They are named for Narayana, a mathematician from India. The Narayana numbers can be expressed in terms of binomial coefficients. An example of a counting problem whose solution can be given in terms of the Narayana numbers N, is the number of expressions containing n pairs of parentheses which are correctly matched and which contain k distinct nestings. For instance, with four pairs of parentheses six sequences can be created which each contain two times the sub-pattern.

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