Generating Functions are a neat tool in the study of recursive sequences.
A generating function is a clothesline on which we hang up a sequence of numbers for display.
— Herbert Wilf, Generatingfunctionology (1994)
The idea is that, given a sequence of numbers 
This is the so called ‘ordinary’ generating function. By examining properties of f(x), we can derive information about the formula for that sequence of numbers.
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