import Data.IntSet(IntSet, size, insert, empty)

a :: Integer -> Int -> Integer
a k 1 = 52 - k
a k n = k*(a k (n-1)) + (52-k)*(a (k+1) (n-1))

s :: Int -> IntSet -> Integer
s 1 xs = fromIntegral $ 52 - (size xs)
s n xs = sum [ s (n-1) (insert t xs) | t <- [1..52] ]

main = do
  let xs = [ a 0 n | n <- [1..5] ]
      ys = [ s n empty | n <- [1..5] ]
  print xs
  print ys
  print (xs == ys)