Denote by $f(n)$ the number of $2\times 2 \times 2$ contingency tables with all 2-dim marginals equal to $n$. What is $f(n)$?
It is easy to see that $f(n)$ is polynomial of degree 4, since it counts the number of integer points in a certain 4-dim polytope. I am just curious to see it written explicitly. Also, do you know of a reference where this polynomial is written?
P.S. Even just the lead cofficient would be of interest, i.e. the volume of this polytope.