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It's Calculus. Very basic calculus. The n! portion means take the arbitrary integer n (from 0 to infinity) and the multiply it by each of the next lower numbers. function factorial($number) { if ($number == 0) return $number; else return $number * factorial($number - 1); } That's how it works. (Arbitrary pseudo-code, I didn't actually test it, but it should work fine.) 0! = 1; 1! = 1 * 0! = 1; 2! = 2 * 1! = 2 * 1 * 0! = 2; 3! = 3 * 2! = 3 * 2 * 1! = 3 * 2 * 1 * 0! = 6; 4! = 4 * 3! = 4 * 3 * 2! = 4 * 3 * 2 * 1! = 4 * 3 * 2 * 1 * 0! = 24; Thanks, EBrown