Best Way to Recursively Find Factorials with Memoization in F#

Question

I wrote this clunky function that works but is not optimal. What is a good way to write a recursive function with memoization to compute factorials in F#? The function can return a dictionary type data structure with the results, or store them in a variable like this function.

open System.Collections.Generic

let factorials = Dictionary<int, int>()
factorials.Add(1, 1)

let rec factorial n =
    if n <= 1 then 1
    else
        match factorials.TryGetValue(n) with
        | true, _  -> n * factorial(n-1)
        | false, _ -> 
            factorials.Add(n, n * factorial(n-1))
            n * factorial(n-1)     

let a = factorial 9

Answer 1

open System.Collections.Generic

let factorials = Dictionary<int, int>()
factorials.Add(1,1)

let factorial n =
    let dictValue : int ref = ref 0
    let rec factorialWithAcc n limit acc =
        match n with
        | x when n > limit -> ()
        | _ -> 
            let acc = acc * n
            if factorials.TryGetValue(n,dictValue) 
            then ()
            else factorials.Add(n,acc)
            factorialWithAcc (n+1) limit acc
    factorialWithAcc 1 n 1

let printFact () =
    let rec printFact n =
        match n with
        | 0 -> ()
        | _ -> 
            printfn "n: %A, %A" n factorials.[n]
            printFact (n-1)
    printFact factorials.Count

let test () = 
    let result = factorial 9
    printFact ()

test ()