Generating function for compositions with odd parts at least 2i-1

[beddytear]

Hi.
I'm really struggling with this generating function problem. Any help would be greatly appreciated.

Question:
Find the generating function for the compositions (c1,c2,c3...,ck) such that for each i, ci is an odd integer at least 2i-1.

Second part of question:

Use the above solution to to find the number of compositions of a positive integer n into k parts (c1,c2...ck) such that for each i, ci is an odd integer at least 2i -1.

 

[HallsofIvy]

The "generating function" for a list of numbers is, by definition, the power series having those numbers as coefficients.