(defun ! (n) (reduce #'* (loop for i from 1 to n collect i)))

(defun C () (* 426880 (rationalize (sqrt 10005))))
(defun M (k) (/ (! (* 6 k)) (! (* 3 k)) (expt (! k) 3)))
(defun L (k) (+ (* 545140134 k) 13591409))
(defun X (k) (expt  -262537412640768000 k))

(defun pi-fraction (k)
  (* (C) (/ 1 (loop for i from 0 to k sum
                 (/ (* (M i) (L i)) (X i))))))                                     

(format t "~a~%" (pi-fraction 10))