(untitled) (European Journal of Pure and Applied Mathematics, 2026)
In this study, we gave a decomposition method used to calculate r-Whitney numbers of the first and second kind in an explicit and non-recursive mode. Then, we expressed the generalized factorial matrices in terms of the rWhitney transform matrix which may be regarded as a generalization in the form of the Vandermonde matrices. Consequently, we presented some properties of the generalized factorial matrices, particularly the triangular matrix factors of their inverse matrices.