I found this question on Yahoo! Answers and I thought it likely someone here would have an answer:
"That is, not counting the order of the sum, in how many ways can you write N as a sum of at most K positive integers (not necessarily unique)? I've known these as 'sub-partition' functions and (I believe) they are (rounded off) polynomials of degree K-1. Does anyone know of a reference giving these polynomials for small values of K?"
Here's the link: How many ways to partition N (identical) items into at most K groups? - Yahoo! Answers