import Data.List
import Data.Ratio

-- slightly altered seidel triangle
seidel :: Integer -> [Integer]
seidel 0 = [1]
seidel 1 = [1]
seidel n
 | odd n = scanr (+) (last helper) helper
 | otherwise = scanl (+) (head helper) helper 
    where helper = seidel (n - 1)

--seidel n = reverse ((head (helper)) : (helper))
-- where helper = scanr1 (+) (seidel (n - 1))

t :: Integer -> Integer
t 0 = 1
t 1 = 1
t n 
 | odd n = last (seidel (n))
 | otherwise = head (seidel (n))

bernoulli :: Integer -> Rational
bernoulli 0 = 1
bernoulli 1 = (-1) % 2
bernoulli n | odd n = 0
bernoulli n | otherwise = (-1) ^ (div n 2) * n * (t (n-1)) % (2^n - 4^n)