import Data.List
import Data.Function (on)
import Data.Char (ord)

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

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