Looking for what this function might be called. I would call it a function that maps a list to its partial reductions.

map-partial-reductions.clj

(defn map-partial-reductions
  "Given a reduce function, an initial value for the reduce, and a list generate a list of partial reductions as it goes"
  [f memo l]
  (reduce #(if (nil? (last %1))
      (conj %1 (f memo %2))
      (conj %1 (f (last %1) %2))) [] l))

; So, for the following
(map-partial-reductions + 0 '(1 2 3 4 5))
; => [1 3 6 10 15]
; so the first value is 1, the second is 1 + 2, the third is 1 + 2 + 3, and so on