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**1. Homework Statement**

I need to find the number of ways to make change for a dollar using an even number of coins, using only pennies, nickels, dimes, quarters, and fifty cent pieces.

**2. Homework Equations**

I found the generating function for the ways of making change for a dollar, 1/(1-x)(1-x^5)(1-x^10)(1-x^25)(1-x^50).

**3. The Attempt at a Solution**

I was thinking of changing the x into an x/2 to ensure that each number of coins is even, but I know that is not right. I am not sure how to ensure that there are an even number of coins. I need to find a new generating function, but am not sure what it is. Any help is appreciated. Thanks