  We introduce an expressive subclass of non-negative almost submodular set
functions, called strongly 2-coverage functions which include coverage and
(sums of) matroid rank functions, and prove that the homogenization of the
generating polynomial of any such function is completely log-concave, taking a
step towards characterizing the coefficients of (homogeneous) completely
log-concave polynomials. As a consequence we obtain that the "level sets" of
any such function form an ultra-log concave sequence.
