_readme.md

I'm trying to calculate the result of a formula. The formula is below in TeX, which generates this:

Running the haskell runs for about 20 minutes, and then runs out of memory and quits.

How can I do this?

maths.tex

\sum_{x=3}^{12}  \left( \sum_{h=0}^3 \left[ \frac{(P(45,x-h)+P(3,h))!}{P(45,x-h)! \times P(3,h)!}   \times 26^{h}\right]   \right)

Unique.hs

import Data.List (foldl1')

-- Factorial function
fact n = foldl1' (*) [1..n]

-- Permutation function
n `p` 0 = 1
n `p` 1 = n
n `p` r = foldl1' (*) [n-r+1..n]

-- Main function
unique :: Integer -> Integer -> Integer
unique c n = c * foldl1' (\acc x -> acc +
    foldl1' (\acc h ->
      let npxh = n `p` (x-h)
          threeph = 3 `p` h
      in acc +
        fact(npxh + threeph) * 26 ^ h
        `div` (fact npxh * fact threeph)
    ) [0..3]
  ) [3..12]

main :: IO ()
--main = print $ unique 6 45
main = print $ unique 2 3