Narayana number ( $N (n, k)$ )

N (n, k) = \frac{1}{n} (k n) (k - 1 n)

counts Dyck paths of semilength

n

with exactly

k

peaks, for

1 \leq k \leq n

. Summing over

k

gives the

n

th Catalan number.

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Narayana number by

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The Narayana numbers are a sequence of numbers that appear in combinatorial mathematics and are related to various counting problems, including those involving paths and combinations.

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