  We show that certain Riordan arrays have generating functions that can be
expressed as continued fractions of Jacobi and Thron type. We investigate the
inverses of such arrays, which in certain circumstances can also have
generating functions representable as continued fractions. Links to orthogonal
polynomial moment sequences, and to Laurent biorthogonal polynomials are
developed. We show that certain Riordan group involutions can be defined by
continued fractions. We also show how simple transformations of the Jacobi
continued fractions can lead to exponential Riordan arrays. Finally, by way of
contrast, we look at the case of some non Riordan arrays that are of
combinatorial significance, including the Narayana numbers.
