Letting
Bn,r be the
n-
th r-Bell polynomial, it is well known
that
Bn(
x) admits specific integer coordinates in the
two bases
and
according to, respectively, the Stirling numbers and the
binomial coefficients. Our aim is to prove that the sequences
Bn+m,r
(
x ) and
Bn,r+s (
x ) admit a binomial recurrence coefficient
in different bases of the
-vector space formed by polynomials of