Reddit mentions of Analytic Combinatorics

You're probably right.

For algorithms, the usual undergraduate text is Introduction to Algorithms by Cormen, et al. I do recommend it, too. It's comprehensive and good.

Besides Cormen, I've also made good use of Analysis of Algorithms and Analytic Combinatorics by Sedgewick and Flajolet. They're a bit more advanced, but I don't know algorithms analysis well enough as a field to know where they would usually be taught or how central their material is. They've been very worthwhile purchases for me, though, and I do recommend them as well.

Edit: It's also worth pointing out that, at my institution, the graduate intro algorithms course used Kozen's other textbook, The Design and Analysis of Algorithms. You might want to take a look.

If I se a movie that I like then I look at other movies with the same director. Have you looked at other books by any of the three? Knuth's Art of Computer Programming comes to mind, for instance.

Another is Analytic Combinatorics (one author is a student of Knuth's).