let memo n f =
  let h = Hashtbl.create n in
  let rec g k = match Hashtbl.find_opt h k with
      Some v -> v
    | None -> let v = f g k in Hashtbl.add h k v; v
  in g
open Num
let rec f n =
  let aux g = function
      0 -> num_of_int 4
    | 1 -> num_of_string "17/4"
    | n -> (num_of_int 108) -/ (num_of_int 815) // g (n - 1) +/ (num_of_int 1500) // (g (n - 1) */ g (n - 2))
  in memo n aux n
let (<<) f g x = f (g x)
let println = print_newline << print_string << approx_num_fix 30
let () =
  println @@ f 0;
  println @@ f 1;
  println @@ f 2;
  println @@ f 3;
  println @@ f 80;
 

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