Applications of Catalan Numbers

In this article, we have explored different applications of Catalan Numbers such as:

number of valid parenthesis expressions
number of rooted binary trees with n internal nodes
number of ways are there to cut an (n+2)-gon into n triangles
How many “mountain ranges” can you form with n upstrokes and n downstrokes
How many paths are there of length 2n that lead from the upper left corner to the lower right corner
Number of ways to tile a stairstep shape of height n with n rectangles
number of Bi...