So given a sequence A0, A1, infinite sequence like the types we were working with recurrences the ordinary generating function of that sequence is obtained by multiplying the Kth term by Z to the K and then summing over old K. We also use the notation that inside brackets Z to the N of A of Z, is the coefficient of Z to the N in A of Z. and a lot of times we want to refer to what the coefficient is. and we'll see how it, it applies, but let's just talk formally about some examples of generating functions first. 