  In this paper, we introduce the $r$-central factorial numbers with even
indices of the first and second kind, as extended versions of the central
factorial numbers with even indices of both kinds. We obtain several
fundamental properties and identities related to these numbers. We show that
the unsigned $r$-central factorial numbers with even indices of the first kind
are strictly log-concave and Poisson-binomially distributed . Finally, we
consider the $r$-central factorial matrices and the factorization of it.
