Try F# Generics

CatalanNumber.fs

open Microsoft.FSharp.Collections
open System.Collections.Generic

let rec fact (n:int64) :int64 =
    if n = 0L then 1L
    else n * fact (n-1L)
               
let comb (n:int64) (r:int64) = 
    let a = fact n
    let b = fact r
    let c = fact (n-r)
    //printfn "f %d %d %d" a b c
    (a / (b*c))
 
let catalan_number (n:int64) :int64 =
    match n with
    | 0L -> 1L
    | _ -> comb(2L*n) n - comb (2L*n) (n-1L)

[<EntryPoint>]
let main argv = 
    printfn  "hello %A" argv

    (*
    printfn "fact %d" (fact 0)
    printfn "fact %d" (fact 2)
    printfn "fact %d" (fact 3)
    printfn "fact %d" (fact 5)
    //*)

    (*
    printfn "comb %b" (comb 2 0 = 1)
    printfn "comb %b" (comb 2 1 = 2)
    printfn "comb %b" (comb 2 2 = 1)

    printfn "comb %b" (comb 3 0 = 1)
    printfn "comb %b" (comb 3 1 = 3)
    printfn "comb %b" (comb 3 2 = 3)
    //*)

    (*
    let ans = [|1; 1; 2; 5; 14; 42; 132; 429; 1430; 4862; 16796; 58786; 208012; 742900; 2674440; 9694845|]
    for index in 0..(ans.Length-1) do
        let i = int64 (index)
        printfn "catalan %d = %d ; %b" i (catalan_number i) (catalan_number i = int64(ans.[index]))
    //*)

    //(*
    printfn "comb %d" (comb 20L 10L)
    printfn "comb %d" (comb 20L 9L)

    printfn "comb %d" (comb 22L 11L)
    printfn "comb %d" (comb 22L 10L)

    printfn "fact %d = %d" 20 (fact 20L)
    printfn "fact %d = %d" 21 (fact 21L)
    printfn "fact %d = %d" 22 (fact 22L)
    //*)
    (*
    printfn "fact %d" (fact 12L)
    printfn "fact %d" (fact 100L)
    //printfn "fact %d" ((fact 14) / ((fact 7) * (fact 7)) )
    //printfn "fact %d" ((fact 14) / ((fact 7) * (fact 8)) )
    //*)

(*
hello [||]
comb 184756
comb 167960
comb -784
comb -719
fact 20 = 2432902008176640000
fact 21 = -4249290049419214848
fact 22 = -1250660718674968576
続行するには何かキーを押してください . . .
*)

    0 // 整数の終了コードします

    ;