A199400 Triangle T(n,k), read by rows, given by (2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...) DELTA (2,1,3,2,4,3,5,4,6,5,7,6,8,7,9,...) where DELTA is the operator defined in A084938.

1, 2, 2, 4, 10, 6, 8, 38, 54, 24, 16, 130, 330, 336, 120, 32, 422, 1710, 3000, 2400, 720, 64, 1330, 8106, 21840, 29400, 19440, 5040, 128, 4118, 36414, 141624, 285600, 312480, 176400, 40320, 256, 12610, 158010, 853776, 2421720, 3900960, 3598560, 1774080, 362880

Offset: 0

Author

Philippe Deléham, Nov 05 2011

Keywords

• nonn
• tabl

Comments

Variant of A162508.

Examples

			Triangle begins :
1
2, 2
4, 10, 6
8, 38, 54, 24
16, 130, 330, 336, 120
32, 422, 1710, 3000, 2400, 720
		

Crossrefs

Cf. A084938, A143494, A162508, A162509,

Formula

T(n,k)=(k+1)!*A143494(n+2,k+2)

T(n,k)=(k+1)*T(n-1,k-1)+(k+2)*T(n-1,k).

Sum_{k, 0<=k<=n} T(n,k)=A162509(n+1).

T(n,n)=(n+1)!=A000142(n+1)

T(n,0)=2^n=A000079(n).