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How does a generating function relate to a sequence of numbers.?

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  • How does a generating function relate to a sequence of numbers.?


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Answer #1 | 23/12 2013 20:44
Generating functions give a sequence of numbers by way of a power series. The coefficients of the series is the sequence of numbers. So for instance the generating function for the unit sequence {1,1,1,1,...} is ∑{n=0,∞} xⁿ = 1 / (1 - x) The fact that the series has a closed form is convenient, but it's not required, and it's pretty rare.

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