Find the coefficients of a rational generating function
Haskell, 63 bytes



z=0:z
(a:b)%y@(c:d)=a/c:zipWith(-)(b++z)(map(a/c*)d++z)%y
_%_=z


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Defines an operator % returning an infinite lazy list of coefficients. The list is zero-indexed, so the constant coefficient is included.