Today I programmed

Binomial Expansion In Clojure

(use 'clojure.contrib.math)

(def factorial
  (fn [n]
    (loop [cnt n acc 1]
       (if (zero? cnt)
            acc
          (recur (dec cnt) (* acc cnt))))))

(defn perm
  "Just the formula for calculating the number of perms given n and k."
  [n k]
  (/ (factorial n) (factorial (- n k))))

(defn choose
  "Just the formula for calculating the number n choose k."
  [n k]
  (/ (perm n k) (factorial k)))
 
(defn binomial-expand
  "The binomial theorem gives a way of expanding binomials raised to the k
   power. This method is far simpler than multipling things out. It is also
   something I spent a little time mulling over. I'm just writing this out so
   that I can get a better feel for it."
  [x y n]
  (apply + (for [k (range 0 (inc n))]
	     (* (choose n k) (expt x (- n k)) (expt y k)))))