  Using the theory of exponential Riordan arrays and orthogonal polynomials, we
demonstrate that the "descending power" Eulerian polynomials, and their once
shifted sequence, are moment sequences for simple families of orthogonal
polynomials, which we characterize in terms of their three-term recurrence. We
obtain the generating functions of the polynomial sequences in terms of
continued fractions, and we also calculate their Hankel transforms.
