binom :: Integer -> Integer -> Integer
binom n k | k < 0 || k > n  = 0
          | 2*k > n         = binom n (n-k)
          | k == 0          = 1
          | otherwise       = binom n (k-1) * (n-k+1) `div` k

catalan :: [Integer]
catalan = 1 : cathelp 1 1
    where cathelp n last = next : cathelp (n+1) next
              where next = (2*n)*(2*n-1) * last
                           `div` ((n+1)*n)

partition :: [Integer]
partition = 1 : [ partition_of k | k <- [1..] ]
    where partition_of k = sum [ sign * (partition !! (k-off))
                                 | (sign, off) <- takeWhile ((<= k) . snd)
                                                            pentagonal_offsets]
          pentagonal_offsets =
            zip (cycle [1,1,-1,-1])
                $ concatMap (\n -> [(3*n-1)*n `div` 2, (3*n+1)*n `div` 2]) [1..]