But I don't know about your big-O estimate. Since the triangle is constructive and you are memoizing calculating n! from n * (n - 1)! will take O(1). It'll be the cached (n - 1)! value times n.
Doing a single multiplication is not O(1) when the numbers have more than a constant number of digits. I'm not precisely sure how long multiplying large numbers takes, but it's at least linear in the number of digits involved. And (n-1)! has O(n log n) digits.
