  We study an infinite class of sequences of sparse polynomials that have
binomial coefficients both as exponents and as coefficients. This generalizes a
sequence of sparse polynomials which arises in a natural way as graph theoretic
polynomials. After deriving some basic identities, we obtain properties
concerning monotonicity and log-concavity, as well as identities involving
derivatives. We also prove upper and lower bounds on the moduli of the zeros of
these polynomials.
