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I have been looking on the net for a textbook that only is about "Generating Functions" but did not found much. Is there any textbook just about "Generating Functions"?

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    Maybe it would be expeditious to say what level of textbook you are seeking, e.g. upper level undergraduate, graduate level, or (?) research survey.2011-02-24

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Try generatingfunctionology.

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Generatingfunctionology is the canonical undergraduate text. The canonical graduate text is Flajolet and Sedgewick's Analytic Combinatorics.