I am working with a generating function in 4 variables; it is a rational function whose denominator is degree 10 which enumerates the number of ways to place electrons (spin up or down) in a linear array and account for Coulomb interactions. Trying to find closed form expression for the general term in the series expansion. Working with a simpler case (3 variables) of the same problem ignoring the spin state, I found the expression to be a product of binomial coefficients and have reason to expect that in the 4-variable problem, the expressions will be similar.