  We study explicit continued fraction expansions for certain series. Some of
these expansions have symmetry that generalizes some remarkable examples
discovered independently by Kmosek and Shallit. Furthermore, we prove the
following theorem: Suppose f(x) is a polynomial with integer coefficients, and
consider the sum of 1/f^n(x) as n goes from 0 to infinity, where f^n denotes
the n-th iterate of f. This series has a continued fraction expansion over the
polynomials. The case when the partial quotients have integer coefficients is
particularly interesting, since then one can obtain simple continued fractions
when one substitutes integer values for x. In this case, the continued fraction
expansion is called specializable. We determine all polynomials f(x) such that
the sum of 1/f^n(x) has a specializable continued fraction: this holds iff f(x)
satisfies one of 14 congruences.
