import Data.List
import Data.Char
import Data.Ratio

bernoulli :: Integer -> Rational
bernoulli 0 = 1
bernoulli 1 = -1 % 2
bernoulli n
  | n `mod` 2 /= 0 = 0
  | otherwise      = sum [fromIntegral (n `choosePerm` k) * (bernoulli k) * (1 % (k - n - 1)) | k <- [0..(n-1)]]

choosePerm :: Integer -> Integer -> Integer
choosePerm n 0 = 1
choosePerm 0 k = 0
choosePerm n k = choosePerm (n-1) (k-1) * n `div` k