Generating Function- change for a dollar

[dancergirlie]

Homework Statement

If our currency consists of a two-cent coin and three kinds of pennies, how
many ways can we make change for a dollar?

Homework Equations

The Attempt at a Solution

the previous part to this problem led to this generating function:

G(x)=(1+x)^3∑_(k≥0)▒〖((k+3)¦3)(〖x^2)〗^k 〗

Am I supposed to put something in for x or for k? I don't know what to do. Any help would be great!

 

[dancergirlie]

that is supposed to be the sum for all k greater than or equal to zero of [((k+3) choose 3)(x^2)^k]