Generating Matrices of C-nomial Coefficients and Their Spectra

In this paper, we consider a generalization of binomial coefficients, called C-nomial coefficients, dependent upon a sequence unn, with indices in arithmetic progressions. We obtain a general recurrence relation and a generating matrix, and point out some new relationships between these coefficients and the generalized Pascal matrices. Further, we obtain generating functions, combinatorial representations, and many new interesting identities and properties of these coefficients.