I was reading Stanley's first volume on Enumerative Combinatorics, and I am seemingly stuck on a basic question regarding compositions. It may be that my algebra skills are rusty, but I just cannot get the correct formula for the number of compositions of n into even numbers of even valued parts. To elaborate, the generating function for the number of compositions of n into k parts where each part is even is ( x^2 + x^4 + x^6 + x^8 ........)^k After we simplify this equation and look at the coefficients of the expanded polynomial, we should be able to get the formula to answer the above question. I have checked many times, but the incorrect answer that I always come up with is (n-k-1 choose n-2k). I was wondering if someone else can try and derive the formula so that I can see what went wrong with my answer?