\begin{abstract}
We prove that three classes of numbers -- the non-central Stirling
numbers of the first kind, generalized factorial coefficients, and
Gould-Hooper numbers -- may be defined by the use of derivatives. We
derive several properties of these numbers from their definitions. We
also prove a result for harmonic numbers.  The coefficients of Hermite
and  Bessel polynomials are a particular case of generalized factorial
coefficients, The coefficients of the associated Laguerre polynomials
are a particular case of Gould-Hooper numbers. So we obtain some
properties of these polynomials. In particular,
we derive an orthogonality  relation for the coefficients of Hermite
and Bessel polynomials.
\end{abstract}
