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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. books.google.com/… –  Phira Nov 6 '11 at 0:02
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I like "Generatingfunctionology" by Wilf. The 2nd edition can be downloaded from math.upenn.edu/~wilf/DownldGF.html. The 3rd edition is available from the publisher. –  marty cohen Nov 6 '11 at 0:17
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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. –  Brian M. Scott Nov 6 '11 at 0:23
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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... –  J. M. Nov 6 '11 at 1:08
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anon guessed correctly, here's an old blog post by Qiaochu somewhat related to this. –  Ragib Zaman Nov 6 '11 at 2:19

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