Here is a rather more general solution than required. The grow-matrix function will grow any N by N matrix into an N+1 x N+1 matrix, using any function of the three leftward/upward neighbors, here labelled "West", "North", and "Northwest". We then define three iterator functions that can grow Pascal matrices, and use those iterators to define three constants, each of which is an infinite sequence of ever-larger Pascal matrices. Normal subscripting then pulls out the ones of the specified size.