-- Three infinite lists, corresponding to the three
-- definitions in the problem statement.

cats1 :: [Integer]
cats1 =
  (div . product . (enumFromTo . (2 +) <*> (2 *)))
    <*> (product . enumFromTo 1) <$> [0 ..]

cats2 :: [Integer]
cats2 =
  1 :
  fmap
    (\n -> sum (zipWith (*) (reverse (take n cats2)) cats2))
    [1 ..]

cats3 :: [Integer]
cats3 =
  scanl
    (\c n -> c * 2 * (2 * n - 1) `div` succ n)
    1
    [1 ..]

main :: IO ()
main = mapM_ (print . take 15) [cats1, cats2, cats3]