x! - [(x-1)!+(x-2)!+(x-3)!...............2!+1!]
Ah, I figured out the mistake in my quickie guess-calculation.
a * b * c - b * c = (a-1) * b * c is true, but a * b * c - c = (a * (b-1) * c) is false. It should = ((a * b) - 1) * c, which doesn't simplify and gets worse the longer the expression is.