Find a closed form expression (i.e., a rational function) for the generating function for the number of ways to make n cents out of nickels, dimes and quarters if you must use an even number of nickels, an odd number of dimes, at least 2 quarters, at most 20 nickels, and at most 12 dimes? Expand the expression showing all nonzero terms through x100. Note: The number of such ways for 80 cents and 85 cents is 2 and 1, respectively