The Narayan number N(n, k) for n = 1, 2, ... and k = 1, ..., n gives a solution to several counting problems in combinatorics. For example, N(n, k) gives the number of expressions with n pairs of parentheses that are correctly matched and contain k distinct nestings. It also gives the number Dyck paths of length n with exactly k peaks. A closed-form expression of N(n, k) is given by N(n, k) = 1/n(n k)(n k - 1), where (n k) is a binomial coefficient.
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