module Stirling where

import Data.MemoTrie

-- Number of ways to partition n into k subsets
secondStirling :: Int -> Int -> Integer
secondStirling = memo2 ss where
    ss n k = if k > n
             then 0
             else if n <= 6
                  then table !! n !! k
                  else (fromIntegral k) * secondStirling (n - 1) k + secondStirling n (k - 1)
    table =
        [ [1]
        , [0, 1]
        , [0, 1, 1]
        , [0, 1, 3, 1]
        , [0, 1, 7, 6, 1]
        , [0, 1, 15, 25, 10, 1]
        , [0, 1, 31, 90, 65, 15, 1] ]