DouKaku?

module Main (main) where

import Data.List
import System.Environment

comb s 0 xs | s == 0    = [xs]
            | otherwise = []
comb s k (x:xs)
  | k * x > s = []
  | otherwise = comb (s-x) (k-1) xs ++ map (x:) (comb s k xs)
comb _ _ _ = []

comb' s k (x:xs)
  | k * x > s = []
  | otherwise = comb (s-x) (k-1) xs
comb' _ _ _ = []

magic n = iterate (concatMap (comb' s n)) [ns] !! n
  where ns = [1..n^2]
        s  = sum ns `div` n

main = print . length . magic . read . head =<< getArgs