Determine in how many ways the amount of 50 can be paid by bank notes of 1, 2, 5, 10, and 20
I have used the generating function that
$G(x)=\frac{1}{1-x}\frac{1}{1-x^2}\frac{1}{1-x^5}\frac{1}{1-x^{10}}\frac{1}{1-x^{20}}$
and $G(x)=\frac{1+x}{1-x^2}\frac{(1+x^5)(1+x^{10)}}{(1-x^{20})^3}$, and then i expand it with two binomial series which product together, and find the answer 450
I want to know whether the answer is correct, and find a easy way to solve it. Thank you.