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

0,3

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

Links

Table of n, a(n) for n=0..44.

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).

Example

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.

Sequence in context: A209691 A221683 A332760 * A141660 A368500 A209699

Adjacent sequences: A199332 A199333 A199334 * A199336 A199337 A199338

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 05 2011

Extensions

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

Status

approved