One very special kind of enumeration method is Series Expansions.
A set of references to review papers on series expansions
can be found at the
Lecture 3 page of my lectures from the 1998 Summer School in Oporto.
Extracts from these are given in the links below. The tables and equations
mentioned below are based on
the column from Computers in Physics,
(J. Adler, ``Series Expansions'', (1994)
Computers in Physics, 8, 287-295.
and this entire article can be downloaded
postscript file .)
Introduction to series expansions
Derivation of one series
Analysis of series