import qualified Data.MemoCombinators as Memo
-- memoizing a function remembers all earlier computed results
-- also known as Dynamic Programming

a114851 = open where
  open = Memo.integral $ \n ->
  -- counts number of open lambda terms of size n
   if n<2 then 0 else                   -- no code shorter than 2 bits
     1 +                        -- encode variable index n-1 in n bits
     open (n-2) +                   -- only count lambda terms if qLam
     sum [open i * open (n-2-i) | i <- [0..n-2]] -- count applications

main = print . map a114851 $ [0..]