  The aim of this paper is to introduce Bell polynomials and numbers of the
second kind and poly-Bell polynomials and numbers of the second kind, and to
derive their explicit expressions, recurrence relations and some identities
involving those polynomials and numbers. We also consider degenerate versions
of those polynomials and numbers, namely degenerate Bell polynomials and
numbers of the second kind and degenerate poly-Bell polynomials and numbers of
the second kind, and deduce their similar results.
