  The cluster cumulant formula of Kubo is derived by appealing only to
elementary properties of subsets and binomial coefficients. It is shown to be a
binomial transform of the grand potential. Extensivity is proven without
introducing cumulants. A combinatorial inversion is used to reformulate the
expansion in the activity to one in occupation probabilities, which explicitly
control the convergence. The classical virial expansion is recovered to third
order as an example.
