In mathematics, given a sequence a_0, a_1, a_2, ..., a_i, ..., the GeneratingFunction is the series:
\sum_{i = 0}^{\infty} a_i x^i.
GeneratingFunctions appear in combinatorics, probability theory, and in theoretical computer science. They often provide good ways of computing a series when simple enumeration would be slow. Examples:

Binomial(n, k), n fixed --> (1 + x)^n FibonacciSequence --> x/(1-x-x^2)Number of ways to make change of k cents given coins worth 1, 5, 10, 25 cents

--> 1/[(1-x)(1-x^5)(1-x^10)(1-x^25)]To use the last, you could try using partial fractions. Unfortunately, that won't work out too well. -- EricJablow

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