Find the generating function

Let $V = \{1, 5, 10, 25, 50, 100\}$. The generating function is \[ \prod_{n \in V} (1+x^n +x^{2n} + \dots) = \prod_{n \in V} \frac{1}{1-x^n}. \] In fact, the coefficient $a_i$ of $x^i$ in the product is the number of ways one can write $i = \sum_{n \in V} b_n \cdot n$ for some choice of non-negative integers $b_n$, which is the same as the number of ways one can pay $i$ cents with the given coins.