I'm new to generating functions. I think I may be missing something and would like it cleared up. This is what I assume:
A generating function is an infinite power series. Assume a sequence $$.
This is also equal to:
For the special case where all $a_i=1$, then:
How is this?
Let's plug in 3 for z into the first formula.
These two are not the same... How can we claim that they are? Am I missing something? Did I break math??? :)