A062323 Triangle with a(n,n)=1, a(n,k)=(n-1)*a(n-1,k)+a(n-2,k) for n>k.

1, 0, 1, 1, 1, 1, 2, 3, 2, 1, 7, 10, 7, 3, 1, 30, 43, 30, 13, 4, 1, 157, 225, 157, 68, 21, 5, 1, 972, 1393, 972, 421, 130, 31, 6, 1, 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1, 56660, 81201, 56660, 24541, 7578, 1807, 350, 57, 8, 1, 516901, 740785, 516901, 223884

Offset: 0

Author

Henry Bottomley, Jul 05 2001

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1;
[1] 0, 1;
[2] 1, 1, 1;
[3] 2, 3, 2, 1;
[4] 7, 10, 7, 3, 1;
[5] 30, 43, 30, 13, 4, 1;
[6] 157, 225, 157, 68, 21, 5, 1;
[7] 972, 1393, 972, 421, 130, 31, 6, 1;
[8] 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1;
		

Links

• Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened

Crossrefs

Essentially the same as A058294, but more easy seen as a triangle. Columns include A001040, A001053, A058307, A058308, A058309. Other sequences appearing on the right hand side include A000012, A001477, A002061, A034262.

Programs

Haskell

a062323 n k = a062323_tabl !! n !! k
a062323_row n = a062323_tabl !! n
a062323_tabl = map fst $ iterate f ([1], [0,1]) where
   f (us, vs) = (vs, ws) where
     ws = (zipWith (+) (us ++ [0]) (map (* v) vs)) ++ [1]
          where v = last (init vs) + 1
-- Reinhard Zumkeller, Mar 05 2013

Formula

a(n, k)=k*a(n, k+1)+a(n, k+2) for n>k.