# Making Change for a Dollar (and other number partitioning problems)

I was trying to solve a problem similar to the "how many ways are there to make change for a dollar" problem. I ran across a site that said I could use a generating function similar to the one quoted below:

The answer to our problem (293) is the coefficient of $x^{100}$ in the reciprocal of the following:

$(1-x)(1-x^5)(1-x^{10})(1-x^{25})(1-x^{50})(1-x^{100})$

But I must be missing something, as I can't figure out how they get from that to $293$. Any help on this would be appreciated.

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