User blog comment:Holomanga/Binomial Hypercubes/@comment-5029411-20151114225230/@comment-39162-20151213221533

That 2 at the end should be a 4

But, as you can see, those are the subfacets of a 2-dimensional hypercube (aka a square). The coefficient of x^2 (=1) is the number of faces in a square, the coefficient of x (=4) is the number of edges in a square, and the coefficient of 1 (=4) is the number of vertices in a square.