  We present a comprehensive insight into counting distributions from the
perspective of the combinants extracted from them. In particular, we focus on
cases where these combinants exhibit oscillatory behavior that can provide an
invaluable new source of information about the dynamics of the process under
study. We show that such behavior can be described only by specific
combinations of compound distributions based on the Binomial Distribution and
provide their analytical forms which can be used in further investigations and
which can be helpful in the analysis of all other types of counting
distributions.
