  Many important special numbers appear in the expansions of some polynomials
in terms of central factorials and vice versa, for example central factorial
numbers, degenerate central factorial numbers, and central Lah numbers which
are recently introduced. Here we generalize this to any sequence of
polynomials. Let P be the space of a sequence of polynomials such that the
degree of the polynomials less than n . The aim of this paper is to study the
central factorial numbers of the second associated with P and of the first kind
associated with P, in a unified and systematic way with the help of umbral
calculus technique. The central factorial numbers associated with P enjoy
orthogonality and inverse relations. We illustrate our results with many
examples and obtain interesting orthogonality and inverse relations by applying
such relations for the central factorial numbers associated with P to each of
our examples.
