Rectangular dissections of a square (Q1101117)

We investigate the problem that how many different ways one can dissect the unit-square into rectangles with prescribed areas \(w_ 1,...,w_ n\). One of our answers is the following: If \(w_ 1,...,w_{n-1}\) are algebraically independent, then the number in question asymptotically equals to \(32(1+o(1))/\pi \sqrt{3}(n!8^ n/n^ 4)\).