two ways to count the number of 1s in all partitions of a given integer

ones-in-partitions.clj

(defn ones-in-partitions
  "Number of 1s in all partitions of an integer n"
  [n]
  (-> (repeat (dec n) 1)
      (clojure.math.combinatorics/partitions)
      (count)))

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(defn partitions
  "Partition function for positive integers."
  []
  (letfn [(p [n]
            (cons 1
                  (lazy-seq
                   (add-series (p (+ n 1))
                               (concat
                                (repeat (- n 1) 0) (p n))))))]
    (cons 1
          (p 1))))

(defn ones-in-partitions'
  "Number of 1s in all partitions of an integer n"
  [n]
  (->> (partitions)
       (take (dec n))
       (reduce +')))