  In this article, the 2-iterated Sheffer polynomials are introduced by means
of generating function and operational representation. Using the theory of
Riordan arrays and relations between the Sheffer sequences and Riordan arrays,
a determinantal definition for these polynomials is established. The
quasi-monomial and other properties of these polynomials are derived. The
generating function, determinantal definition, quasi-monomial and other
properties for some new members belonging to this family are also considered.
