A hungry math major visits the school's cafeteria and wants to know the number of ways sk to take k servings of food, including at least one main course, an even number (possibly zero) of side vegetables, an odd number of rolls, and at least two desserts. The cafeteria's food can be distinguished only in the coarsest way: Every dish is either a main course, a side vegetable, a roll, or a dessert. There is an unlimited supply of each kind of dish available.
I want to determine a closed form for the generating functions, but I'm not sure how to dertermine the combinatorical interpretation.