Find the generating function G(x) enumerates the number of options to change a dollar using an odd number of nickels, a prime number (0 and 1 excluded) of dimes, and any number of quarters.
Here's the generating function I found: $$G(x) = (x^5+x^{15}+x^{25}+\dots)(x^{20}+x^{30}+\dots)(x^{25}+x^{50}+\dots)$$
Is that look correct? It looks different from the functions that could be reduced as a closed form. In this case we're not adding infinite terms, so should I multiply them out to get the coefficient until $^{100}$? Thanks!