TITLE: Finding the power series of a rational function
QUESTION [12 upvotes]: In many combinatorial enumeration problems it is possible to find a rational generating function (i.e. the quotient of two polynomials) for the sequence in question. The question is - given the generating function, how can we find (algorithmically) the values of the sequence, i.e. the coefficients of the corresponding power series?
I know that for a rational generating function, the sequence satisfies a recurrence relation given by the coefficients of the polynomial in the denominator, so it's really just the question of finding the finite initial values.

REPLY [4 votes]: Sometimes partial fractions decomposition is useful. Especially if there are only simple poles, since then each partial fraction can be expanded in a geometric series.