--     n      m      f(n,m )
sum_ :: Int -> Int -> (Int -> Int -> Int) -> Int
sum_ k j f
    | j <= k = f k j + sum_ k (j+1) f
    | otherwise = 0 

-- from http://stackoverflow.com/questions/28896626/tail-recursive-binomial-coefficient-function-in-haskell
binom :: Int -> Int -> Int
binom n 0 = 1
binom 0 k = 0
binom n k = binom (n-1) (k-1) * n `div` k
    
fak :: Int -> Int
fak n
    | n > 1 = n* fak ( n-1)
    | otherwise = 1

stirling2 :: Int -> Int -> Int
stirling2 n k = (sum_ k 0 (\ k j -> (pot (-1) (k-j)) * (binom k j) * (pot j n) )) `div` (fak k)

pot :: Int -> Int -> Int
pot base exp
    | exp >= 1 = base * pot base (exp-1)
    | otherwise = 1