import Control.Arrow
import Data.List
import Data.Ord
import Data.Ratio

-- Faulhaber's triangle, n-th row, first coefficient.
bernoulli :: Integer -> Rational
bernoulli n = (-1)^n * head (foldl (\rs i -> let xs = zipWith ((*) . (i %)) [2 ..] rs in 1 - sum xs : xs) [] [0..n])