Web Reference: In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series. A generating function is a di erent, often compact way, of writing a sequence of numbers. Here we will be dealing mainly with sequences of numbers (an) which represent the number of objects of size n for an enumeration problem. This will turn out to be helpful in finding generating functions as well. The sequence of differences is often simpler than the original sequence. So if we know a generating function for the differences, we would like to use this to find a generating function for the original sequence.
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