Money exchange solver in Racket - fast version

#lang racket

(define coins (vector-immutable 50 25 10 5 1))
(define coins-amount (vector-length coins))
(define cache-width 1000001)
(define cache (make-vector (* cache-width (add1 coins-amount)) #f))

(define (count-exchanges sum coin-index)
  (let* ([index (+ sum (* coin-index cache-width))]
         [entry (vector-ref cache index)]
         [result
          (cond [entry entry]
                [(zero? sum) 1]
                [(negative? sum) 0]
                [(>= coin-index coins-amount) 0]
                [else
                 (begin
                   (let find-smaller-coin ()
                     (when (and (< coin-index coins-amount)
                                (< sum (vector-ref coins coin-index)))
                       (set! coin-index (add1 coin-index))
                       (find-smaller-coin)))
                   (+ (count-exchanges (- sum (vector-ref coins coin-index)) coin-index)
                      (count-exchanges sum (add1 coin-index))))])])
    (unless entry
      (vector-set! cache index result))
    result))

(time (count-exchanges 1000000 0))