  The connection between a Taylor series and a continued-fraction involves a
nonlinear relation between the Taylor coefficients $\{ a_n \}$ and the
continued-fraction coefficients $\{ b_n \}$. In many instances it turns out
that this nonlinear relation transforms a complicated sequence $\{a_n \}$ into
a very simple one $\{ b_n \}$. We illustrate this simplification in the context
of graph combinatorics.
