# Catalan number

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The Catalan numbers give the number of ways to tile an n-sized stair case with exactly n rectangles.

Catalan Numbers

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Math Encounters -- A Surreptitious Sequence: The Catalan Numbers

Cn (the nth Catalan number) is, among other things, the number of monotonic paths along the edges of a grid with n × n square cells, which do not pass above the diagonal. A monotonic path is one which starts in the lower left corner, finishes in the upper right corner, and consists entirely of edges pointing rightwards or upwards. The diagrams show the case for n = 4:

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Catalan number 4x4 grid example.svg

The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series)

Numbers are arithmetical values and in the programming world numbers and series play a very vital role. Few of the famous numbers & series are Fibonacci series, Catalan number & Binomial Coefficient.

Catalan Numbers