  J.~Lepowsky and R.~L.~Wilson initiated the approach to combinatorial
Rogers-Ramanujan type identities via vertex operator constructions of standard
(i.e. integrable highest weight) representations of affine Kac-Moody Lie
algebras. A.~Meurman and M.~Primc developed further this approach for
$\mathfrak{sl}(2,\mathbb C)\widetilde{}\ $ by using vertex operator algebras
and Verma modules. In this paper we use the same method to construct
combinatorial bases of basic modules for affine Lie algebras of type
$C_{n}\sp{(1)}$ and, as a consequence, we obtain a series of Rogers-Ramanujan
type identities. A major new insight is a combinatorial parametrization of
leading terms of defining relations for level one standard modules for affine
Lie algebra of type $C_{n}\sp{(1)}$.
