  The Carrell-Chapuy recurrence formulas dramatically improve the efficiency of
counting orientable rooted maps by genus, either by number of edges alone or by
number of edges and vertices. This paper presents an implementation of these
formulas with three applications: the computation of an explicit rational
expression for the ordinary generating functions of rooted map numbers with a
given positive genus, the construction of large tables of rooted map numbers,
and the use of these tables, together with the method of A. Mednykh and R.
Nedela, to count unrooted maps by genus and number of edges and vertices.
