Hyperholomorphic Appell polynomials provide a natural extension of classical Appell polynomial sequences within the framework of Clifford analysis, combining algebraic, analytic, and combinatorial aspects. In this talk, we present the construction of a hyperholomorphic family that generalizes the usual complex powers and investigate the structure and characterization of their coefficients. We show that these coefficients display striking combinatorial patterns and are closely related to classical number sequences, including the Vietoris and Wigner numbers. These connections offer new insights into the interplay between hypercomplex function theory and combinatorics, while pointing to potential applications in the theory of special functions and discrete mathematics.