module Exercise_3 where

import Data.Ratio
import Data.List

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

bernoulli :: Integer -> Rational
bernoulli n 
   | (n/=1) && (mod n 2 == 1) = 0
   | otherwise                = sum [sum [ ((-1)^v)*(choose k v)*(v^n)%(k+1) | v<-[0..k]] | k<-[0..n]]