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In spite of having done some exercises, I still find it harder to understand exponential generating function deeply than ordinary generating function. Could someone explain it "deeply"? Or are there any articles on that?

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    I suggest that you either read the book by Bergeron, Labelle and Leroux or that you ask a more precise question. The book might help to convince you that egfs are simpler than ogfs. http://books.google.com/books?id=83odtWY4eogC&printsec=frontcover&dq=labelle+species&hl=de&ei=Cc61TuDANsqWhQfGxOGaBA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q&f=false2011-11-06
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    Hmm. The Wikipedia page on [symbolic combinatorics](http://en.wikipedia.org/wiki/Symbolic_combinatorics) might be helpful, though I suppose you could say it's terse. No doubt user Qiaochu has some posts laying around somewhere or other on this topic.2011-11-06
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    I like "Generatingfunctionology" by Wilf. The 2nd edition can be downloaded from http://www.math.upenn.edu/~wilf/DownldGF.html. The 3rd edition is available from the publisher.2011-11-06
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    Chapter $3$ of Miklós Bóna’s *Introduction to Enumerative Combinatorics* gives a nice introductory sense of the respective contexts in which egf’s and ogf’s are useful.2011-11-06
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    Think of it this way: there are situations where the EGF is simple/easy to manipulate when the OGF is unwieldy or has no closed form, and vice-versa...2011-11-06
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    anon guessed correctly, [here's](http://www.artofproblemsolving.com/blog/10601) an old blog post by Qiaochu somewhat related to this.2011-11-06

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