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We show that certain Riordan arrays have generating functions that can beexpressed as continued fractions of Jacobi and Thron type. We investigate theinverses of such arrays, which in certain circumstances can also havegenerating functions representable as continued fractions. Links to orthogonalpolynomial moment sequences, and to Laurent biorthogonal polynomials aredeveloped. We show that certain Riordan group involutions can be defined bycontinued fractions. We also show how simple transformations of the Jacobicontinued fractions can lead to exponential Riordan arrays. Finally, by way ofcontrast, we look at the case of some non Riordan arrays that are ofcombinatorial significance, including the Narayana numbers.

Riordan arrays and Jacobi and Thron continued fractions