  In this paper we describe each coefficient of the Siegel series associated to
a quadratic $\mathfrak{o}$-lattice $L$ in terms of lattice counting problems,
where $\mathfrak{o}$ is the ring of integers of a non-Archimedean local field
of characteristic $0$. Under the restriction that $p$ is odd and that the
dimension of the radical of the quadratic space $L\otimes\kappa$ on the residue
field $\kappa$ is at most $2$, we provide explicit values of coefficients and
reprove the functional equation of the Siegel series.
