Generating functions are one of the most surprising, useful, and clever inventions in discrete mathematics.

Generating functions transform problems about sequences into problems about functions.

For example:

* sequence {1, 4, 9, 16, 25, ... }

* closed form a(n) = n^2

* generating function: F(x)=x(1+x)/(1-x)^3.

Interested? An introduction to generating functions (pdf document) can be found [ here ].

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