A228340 Triangle read by rows: T(n,k) = (n-1)*T(n-1,k) + T(n-2,k), with T(n,n-1)=1, T(n,n-2)=n-2, for n >= 1, 0 <= k <= n-1.

1, 0, 1, 1, 1, 1, 3, 4, 2, 1, 13, 17, 9, 3, 1, 68, 89, 47, 16, 4, 1, 421, 551, 291, 99, 25, 5, 1, 3015, 3946, 2084, 709, 179, 36, 6, 1, 24541, 32119, 16963, 5771, 1457, 293, 49, 7, 1, 223884, 293017, 154751, 52648, 13292, 2673, 447, 64, 8, 1

Offset: 1

Author

N. J. A. Sloane, Aug 29 2013

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
1,
0,1,
1,1,1,
3,4,2,1,
13,17,9,3,1,
68,89,47,16,4,1,
421,551,291,99,25,5,1,
3015,3946,2084,709,179,36,6,1,
...
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of table, flattened
• C. Cannings, The Stationary Distributions of a Class of Markov Chains, Applied Mathematics, Vol. 4 No. 5, 2013, pp. 769-773.

Crossrefs

Diagonals give A058307, A058279, A228341. Row sums give A001040.

Programs

Haskell

a228340 n k = a228340_tabl !! (n-1) !! k
a228340_row n = a228340_tabl !! (n-1)
a228340_tabl = map (reverse . fst) $ iterate f ([1], [1,0]) where
   f (us, vs'@( : vs@(v : ))) = (vs', ws) where
     ws = 1 : (v + 1) : zipWith (+) us (map (* (v + 2)) vs)
-- Reinhard Zumkeller, Aug 31 2013