The polynomials φ n ( x ; a , b ) {\varphi _n}(x;a,b) of degree n defined by the equations \[ Δ a φ n ( x ; a , b ) = ( x ) n − 1 , b b n − 1 ⋅ ( n − 1 ) ! and Δ b φ n ( x ; a , b ) = φ n − 1 ( x ; a , b ) {\Delta _a}{\varphi _n}(x;a,b) = \frac {{{{(x)}_{n - 1,b}}}}{{{b^{n - 1}} \cdot (n - 1)!}}\quad {\text {and}}\quad {\Delta _b}{\varphi _n}(x;a,b) = {\varphi _{n - 1}}(x;a,b) \] where ( x ) n , b = x ( x − b ) ( x − 2 b ) ⋯ ( x − n b + b ) {(x)_{n,b}} = x(x - b)(x - 2b) \cdots (x - nb + b) is the generalized factorial and Δ a f ( x ) = f ( x + a ) − f ( x ) {\Delta _a}f(x) = f(x + a) - f(x) , are the subject of this paper. A representation of these polynomials as a sum of generalized factorials is given. The coefficients, B ( n , s ) B(n,s) , s = a / b s = a/b , of this representation are given explicitly or by a recurrence relation. The generating functions of φ n ( x ; a , b ) {\varphi _n}(x;a,b) and B ( n , s ) B(n,s) are obtained. The limits of φ n ( x ; a , b ) {\varphi _n}(x;a,b) as a → 1 a \to 1 , b → 0 b \to 0 or a → 0 a \to 0 , b → 1 b \to 1 and the limits of B ( n , s ) B(n,s) as s → ± ∞ s \to \pm \infty or s → 0 s \to 0 are shown to be the Bernoulli polynomials and numbers of the first and second kind, respectively. Finally, the generalized factorial moments of a discrete rectangular distribution are obtained in terms of B ( n , s ) B(n,s) in a form similar to that giving its usual moments in terms of the Bernoulli numbers.