A199335 Triangle T(n,k), read by rows, given by (0,1,0,2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...) DELTA (2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...), where DELTA is the operator defined in A084938.

1, 0, 2, 0, 2, 4, 0, 2, 14, 8, 0, 2, 36, 66, 16, 0, 2, 82, 342, 262, 32, 0, 2, 176, 1436, 2416, 946, 64, 0, 2, 366, 5364, 16844, 14394, 3222, 128, 0, 2, 748, 18654, 99560, 156190, 76908, 10562, 256

Offset: 0

Author

Philippe Deléham, Nov 05 2011

Keywords

• nonn
• tabl

Comments

Following an observation by Dale Gerdemann, it appears that T(n,k) = A120434(n+1,n-k) for n>=1, k>=1. - M. F. Hasler, Apr 18 2015

See also A144696. - Antti Karttunen, Apr 21 2015

Examples

			Triangle begins :
1
0, 2
0, 2, 4
0, 2, 14, 8
0, 2, 36, 66, 16
0, 2, 82, 342, 262, 32
0, 2, 176, 1436, 2416, 946, 64
		

Crossrefs

Cf. A120434, A084938, A005649, A144696.

Formula

Sum_k{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A000142(n+1), A162509(n+1) for x=0,1,2 respectively.

Sum_{k, 0<=k<=n} T(n,k)^2^(n-k) = A005649(n).

Extensions

Typo in 8th row corrected by Olivier Gérard, Oct 29 2012