clusters-sizes.clj

(defn sizes[k n]
  (condp = k
    n #{(vec (repeat k 1))}
    1 #{[n]}
    (reduce (fn [res s0]
              (reduce #(conj % (sort (conj %2 s0)))
                      res
                      (sizes (dec k) (- n s0))))
            #{}
            (take (- n k)(iterate inc 1)))))

(sizes 3 10)