Nothing to add to this except to say that Generatingfunctionology is an awesome book. Although I haven't read it, another in the same space is A=B, also co-aut

Nothing to add to this except to say that Generatingfunctionology is an awesome book. Although I haven't read it, another in the same space is A=B, also co-authored by Wilf (https://www.math.upenn.edu/~wilf/AeqB.html https://www.math.upenn.edu/~wilf/AeqB.html) (another co-author is Zeilberger, whose name anyone interested in computational discrete math will recognise).