*scratch*.el

(defun catalan-next-row (v)
  (if (or (null v)
          (= (length v) 0))
      [1]
    (let ((r (make-vector (1+ (length v)) 1)))
      (dotimes (x (length v))
        (unless (= x 0)
          (setf (aref r x)
                (+ (aref v x)
                   (aref r (1- x))))))
      (setf (aref r (length v))
            (aref r (1- (length v))))
      r)))

(defun catalan-triangle (nrows)
  (let ((row [1]) result)
    (dotimes (i nrows)
      (setf row (catalan-next-row row))
      (push row result))
    (reverse result)))

(insert (prin1-to-string (catalan-triangle 10)))

;; ([1 1]
;;  [1 2 2]
;;  [1 3 5 5]
;;  [1 4 9 14 14]
;;  [1 5 14 28 42 42]
;;  [1 6 20 48 90 132 132]
;;  [1 7 27 75 165 297 429 429]
;;  [1 8 35 110 275 572 1001 1430 1430]
;;  [1 9 44 154 429 1001 2002 3432 4862 4862]
;;  [1 10 54 208 637 1638 3640 7072 11934 16796 16796])