That is why I present it as an absolute value... |n-1|!
|0 - 1|! = 1
It's a "kludge" (aka "a workaround"), CRGreathouse. Nothing more and nothing less. The purpose of the kludge? To preserve symmetry. Not mathematical symmetry, mind you, but (forgive the philosophical turn here...) cognitive symmetry.
a*b = x
x/b = a
... "wrong" for b = 0, a mathematical "fact." I know that.
But practically speaking, it gets in the way of any "number mappings" that start at 0 rather than 1. Which, in large part, is also why I include 1 as the 0-th prime (p'_0). It provides a reference point for comparison with other integer progressions.