Specifically, I want to find the number of integer partitions of 1000 into exactly 100 parts of sizes {5, 20, 100} ignoring different orderings. I am trying to find the generating function. I have seen other answers using $[x^n]$ which I think is referring to the q-analog but I am not sure. I am a little fuzzy on that topic so if someone could explain it, I would greatly appreciate it.
I would also like to know how to do this in general.