import Data.List
import Data.Ratio

choose :: Integer -> Integer -> Integer
n `choose` k = product [n-k+1..n] `div` product [1..k]

bernoulli :: Integer -> Rational
bernoulli n
 | n == 0 = 1
 | otherwise = sum [((choose n k) % (k - n - 1)) * (bernoulli k) | k<-[0..(n-1)]]