Recurrence relations for the Sheffer sequences

In this paper, using the production matrix of an exponential Riordan array [g(t), f(t)], we give a recurrence relation for the Sheffer sequence for the ordered pair (g(t), f(t)). We also develop a new determinant representation for the general term of the Sheffer sequence. As applications, determinant expressions for some classical Sheffer polynomial sequences are derived.