Let's call it a staircase of height n, a figure consisting from all square cells n×n lying no higher diagonals (the figure shows a staircase of height 4 ). In how many different ways can a staircase of height n can be divided into several rectangles whose sides go along the grid lines, but the areas are different in pairs?
https://cdn.artofproblemsolving.com/attachments/f/0/f66d7e9ada0978e8403fbbd8989dc1b201f2cd.png combinatoricscombinatorial geometry