When one first encounters factorials, it often is the case that one uses them to calculate ratios of factorials, the simplest bing n!/(n-1)! = n. This example is a natural one to think about recursively. The comparable examples for sums would be the difference of two sums ... and this is rarely done (except perhaps in the case of proofs of the sum of integers from 1 to n, etc.)
It was clear to me as a child of maybe 8. Granted, in this day and age it's much easier to come up with elementary math, but I would say that particular equation meets the obviousness criterion of patent law, based on the aforementioned historical evidence.
