I have NEVER taken a combinatorics course, outside of what one covers in a calculus-based probability course.
I would be interested in knowing what would be a suitable combinatorics text for studying for the Math GRE Subject Test. Specifically, I'm interested in a text which goes through combinatorics in tandem with linear algebra, abstract algebra, and real analysis (e.g., see this question: How many distinct partials of order $k$ for a function $f: \mathbb{R}^{n}\rightarrow\mathbb{R}$?), and has many practice problems.
Maybe what I'm hoping for doesn't exist. But I have some hope. I've considered Concrete Mathematics, but I'm not sure if it has what I'm looking for.
Having studied for the math GRE two years ago with good results, I'd suggest that you don't need any such text. There won't be more than two or three such problems on a usual test, so it's a highly inefficient use of your time if you don't want the combinatorics for its own sake.
EDIT: the official breakdown is here. Combinatorics is one of five subjects mentioned in three bullets making up together a quarter of the test.