Question 1099746
The Catalan numbers (1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, ...), named after Eugène Charles Catalan (1814–1894), arise in a number of problems in combinatorics. 

Among other things, the Catalan numbers describe:

the number of ways a polygon with n+2 sides can be cut into n triangles
the number of ways to use n rectangles to tile a stairstep shape (1, 2, ..., n−1, n).
the number of ways in which parentheses can be placed in a sequence of numbers to be multiplied, two at a time
the number of planar binary trees with n+1 leaves
the number of paths of length 2n through an n-by-n grid that do not rise above the main diagonal