Solution for math problem

GirardNewton.hs

-- Haskell version of formulae from
-- https://youtu.be/4FNCIYD8HdA

import Control.Monad (join)
import Data.Ratio

oneS :: [Rational]
oneS = join $ repeat [1, (-1)]

pSum :: Int -> Rational
pSum 1 = 1
pSum 2 = 2
pSum 3 = 3
pSum n = sum (zipWith (*) oneS (map (\k -> pSum (n - k) * eSum k) [1 .. (n - 1)])) + fromIntegral n * (oneS !! n) * eSum n

eSum :: Int -> Rational
eSum 0 = 1
eSum 1 = 1
eSum n | n > 3 = 0
eSum n = sum (zipWith (*) oneS (map (\k -> pSum k * eSum (n - k)) [1 .. n])) / fromIntegral n

-- now try
-- pSum 4
-- pSum 5