The method of coefficients

The paper gives an account of the "method of coefficients" due to G. P. Egorychev. The method is used, often without any explicit reference, in the practice of formal power series and generating functions, both in combinatorics and in the analysis of algorithms. Here we show how we can start with a restricted series of general rules and proceed to obtain many results in these fields. Special emphasis is given to the rules of convolution, composition, and inversion, and to the evaluation of combinatorial sums.