generatingfunctionology
TL;DR — Wilf’s text on generating functions — released free by its author, and the standard introduction.
⬇ Download the archived copy — kept here so the document survives its source going dark. Explicitly free / author-released / CC.
University of Pennsylvania. Copyright 1990 and 1994 Academic Press; this is the author’s free Internet Edition.
The standard introduction to generating functions — encoding a sequence as the coefficients of a formal power series so that combinatorial problems become algebraic ones. Wilf’s opening line, that a generating function is “a clothesline on which we hang up a sequence of numbers for display,” is the best one-sentence explanation there is.
Released free by an author who could have kept it behind a publisher, and one of the earliest examples of that choice.
Where this came from
231 pages. A copy is archived locally against link rot; the header links the original source.