Suppose there are these coins: 1c, 5c, 10c, 25c, \$1 (100c) and \$2 (200c). How many different ways can \$2 be made using any number of coins?
I figure we need to use generating functions, so let $C(x)$ be the generating function: $$ C(x)=\frac{1}{(1-x)(1-x^{5})(1-x^{10})(1-x^{25})(1-x^{100})(1-x^{200})} $$
How to compute (like an algorithm) the coefficient of $ x^{200} $?
This question is similar to number of ways to make $2.00 but no computing the solution there.