In the situation where differences between consecutive squares, (or consecutive cubes, consecutive x^4, etc.) are calculated, then the differences between those differences are calculated, and then the differences of those differences, and so on until you reach a constant number at a deep enough level, which is equal to n! (n being the exponent that produced the initial numbers) Is there some type of proof or explanation why it happen to be a factorial value? Is it involved with calculus, since it is similar to transforming a function into a derivitive function, and continuing to find the derivitive? Example: F(x)=x^5 F'(x)=5x^4 F''(x)=5*4x^3 F'''(x)=5*4*3x^2 F''''(x)=5*4*3*2x F'''''(x)=5*4*3*2*1=120=5!