  Enumerating ramified coverings of the sphere with fixed ramification types is
a well-known problem first considered by A. Hurwitz. Up to now, explicit
solutions have been obtained only for some families of ramified coverings, for
instant, those realized by polynomials in one complex variable. In this paper
we obtain an explicit answer for a large new family of coverings, namely, the
coverings realized by simple almost polynomials, defined below. Unlike most
other results in the field, our formula is obtained by elementary methods.
