The Catalan numbers give the number of ways to tile an n-sized stair case with exactly n rectangles.
Catalan number 4x4 grid example.svg
910 is the generalized Catalan number C(11,4).
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The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series)
Catalan Numbers - how many ways of cutting n-polygon into n-2 trianlges