  An Engel series is a sum of the reciprocals of an increasing sequence of
positive integers, which is such that each term is divisible by the previous
one. Here we consider a particular class of Engel series, for which each term
of the sequence is divisible by the square of the preceding one, and find an
explicit expression for the continued fraction expansion of the sum of a
generic series of this kind. As a special case, this includes certain series
whose continued fraction expansion was found by Shallit. A family of examples
generated by nonlinear recurrences with the Laurent property is considered in
detail, along with some associated transcendental numbers.
