Haskell: memoization

Question

I\'m trying to relearn Haskell, after many years away and forgetting everything, and I find myself still confused my memoization. In particular, I\'m trying to write a

Answer 1

With

nders :: Int -> Integer
nders n = (map der [0 ..]) !! n
  where der 0 = 1
        der 1 = 0
        der n = (nders (n-2) + nders (n-1)) * toInteger (n-1)

the map der [0..] part will be recomputed for any application of nders, especially including the recursive calls in der.

You can move out the definition of the tabulation so that it doesn't (syntactically) depend on n, which should do the right thing:

nders :: Int -> Integer
nders = (memoized !!)
  where 
    memoized = map der [0 ..]

    der 0 = 1
    der 1 = 0
    der n = (nders (n-2) + nders (n-1)) * toInteger (n-1)