The paper is devoted to a special polynomial sequence of binomial type in \((n+1)\) real variables with values in the real vector space of paravectors in a Clifford algebra. It is shown that here the matrix multiplication admits a type of factorization that overcomes the restrictions of non-commutativity and solves some problems connected with a special sequence. The study starts with a nice introduction in the topic, presenting the necessary notions and a generalized areolar derivative in the sense of \textit{D. Pompéiu} [Rend. Circ. Mat. Palermo 33, 108--113 (1912; JFM 43.0481.01)]. In the second section of the paper, a sequence of homogeneous monogenic polynomials with coefficients in a Clifford algebra is analyzed. Some representations of a paravector-valued sequence are considered in the third section. From the variety of such representations, the authors are interested in the representation in terms of the paravector and its conjugate, the determinant representation in terms of the real part and the vector part of the paravector, and the complex-like representation, which also implies a matrix representation of the polynomial sequence of binomial type similar to the matrix representation of a complex number. The main result of the fourth section (Theorem 5) describes a matrix recurrence formula and gives some applications for the considered homogeneous polynomials. In the last section of the paper, applications to the construction of Appell sequences are considered.