So, for example, these two generating functions that we've developed here if we subtract the say we subtract the first one from the second, 1u200bz-u200b1/u200b1-u200bz over, one - 2Z - one / one - Z that's the generating function for powers of 2-1. so with each one of these operations we enrich the set of sequences that we know generating functions for. differentiation that's another thing, if we have a generating function A of Z = A K Z to the K, if we differentiate that. 