Gauss's Backward Formula

This is sometimes knows as the "bars and stars" method. Suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility is an arrangement of 5 spices (stars) and 9 dividers between categories (bars). The number of possibilities is . means you use spices 1, 1, 5, 6, and 9.

(1)

for , where is the central difference and

			(2)
			(3)

where is a binomial coefficient.