content: import Data.Array
  
  choose :: Integer -> Int -> Integer
  choose m k = let kk = toInteger k in (product [m..m+kk-1]) `div` (product [1..kk])
  
  max_branches = 4
  max_nodes = 200
  
  bcache = listArray (0, max_nodes)
  	[sum[rcache!n!b!r | r <- [0..n], b <- [0..max_branches-1]] | n <- [0..max_nodes]]
  build_block = (bcache !)
  
  rcache = listArray (0,max_nodes) [arr_b i | i <- [0..max_nodes]] where
  	arr_b n = listArray(0,max_branches) [arr_r b n | b <- [0..max_branches]]
  	arr_r b n = listArray(0,n) [rooted n b r | r <- [0..n]]
  
  rooted 1 0 0 = 1
  rooted 1 _ _ = 0
  rooted _ 0 _ = 0
  rooted _ _ 0 = 0
  rooted n b r
  	| (n <= b) || (n <= r) = 0
  	| otherwise = sum [(firsts b1) * (rests b1) | b1 <- [1..b], r * b1 < n] where
  		firsts = choose (build_block r)
  		rests bb = sum [rcache!(n-r*bb)!(b - bb)!r1 | r1 <- [0..r-1], r1 < (n-r*bb)]
  
  unrooted n = unicenter + bycenter where
  	unicenter = sum [ rcache!n!b!r | b <- [0..max_branches], r <-[0..n], r * 2 < n]
  	bycenter| odd n = 0
  		| otherwise = x * (x + 1) `div` 2 where x = build_block (n `div` 2)
  
  main = mapM_ print $ map (\x->(x, unrooted x)) [1..max_nodes]
  