I think it's fine to get a technical book. If he has two, your father can give away the one his kid didn't inscribe.
I don't know combinatorics well enough to identify the classics (although I do recall having been told that Lovasz's Combinatorial Problems & Exercises is one of the great books of the genre). Instead I offer a few generic suggestions:
Aigner, Ziegler & Hoffman, Proofs From The Book.
Monastyrsky, Modern Mathematics In Light of The Fields Medal.
Edit: I recall having been told that Lovasz's Combinatorial Problems & Exercises can be considered a classic in combinatorics.