Find the generating function
We have coins of these types: 1, 5, 10, 25, 50 cents and $1.
Find the generating function $\sum_{i=0}^{\infty } a_{i} x^{i} $ where $a_{i}$ is the number of ways you can pay $i$ cents with the coins.
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What is the meaning of ∏ here?

It's the product. Just like Σ, but it's a product instead.
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