This is a generic generating functions problem, and you are left with 1/(x-1)(x^5-1)....(x^50-1) however now I want to find the coefficient of the x^100 term of this expression... how can I do this or do I have to use partial fractions which will take ages...
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$\begingroup$See . This site shows how the answer is obtained with just some intelligent counting. Despite the title of the site Frank Morgan suggests $292$ ways, not counting a dollar coin.
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