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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.
2

%I #17 Apr 21 2015 01:05:03

%S 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,

%T 2416,946,64,0,2,366,5364,16844,14394,3222,128,0,2,748,18654,99560,

%U 156190,76908,10562,256

%N 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.

%C 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

%C See also A144696. - _Antti Karttunen_, Apr 21 2015

%F 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.

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

%e Triangle begins :

%e 1

%e 0, 2

%e 0, 2, 4

%e 0, 2, 14, 8

%e 0, 2, 36, 66, 16

%e 0, 2, 82, 342, 262, 32

%e 0, 2, 176, 1436, 2416, 946, 64

%Y Cf. A120434, A084938, A005649, A144696.

%K nonn,tabl

%O 0,3

%A _Philippe Deléham_, Nov 05 2011

%E Typo in 8th row corrected by _Olivier Gérard_, Oct 29 2012