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Triangle, read by rows, given by [0,1,1,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
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%I #7 Aug 11 2015 06:24:23

%S 1,0,2,0,2,2,0,4,2,2,0,8,4,2,2,0,16,8,4,2,2,0,32,16,8,4,2,2,0,64,32,

%T 16,8,4,2,2,0,128,64,32,16,8,4,2,2,0,256,128,64,32,16,8,4,2,2,0,512,

%U 256,128,64,32,16,8,4,2,2,0,1024,512,256,128,64,32,16,8,4,2,2,0,2048,1024

%N Triangle, read by rows, given by [0,1,1,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

%F Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A084247(n), A000007(n), A000079(n), A001787(n+1), A166060(n), A165665(n), A083585(n) for x= -1, 0, 1, 2, 3, 4, 5 respectively. Sum_{k, 0<=k<=n} T(n,k)*x^(n-k) = A040000(n), A000079(n), A095121(n), A047851(n), A047853(n), A047855(n) for x = 0, 1, 2, 3, 4, 5 respectively.

%F G.f.: (1-2*x+x*y)/((-1+2*x)*(x*y-1)). - _R. J. Mathar_, Aug 11 2015

%e Triangle begins :

%e 1,

%e 0,2,

%e 0,2,2,

%e 0,4,2,2,

%e 0,8,4,2,2,

%e 0,16,8,4,2,2,

%e 0,32,16,8,4,2,2,

%e 0,64,32,16,8,4,2,2,

%e 0,128,64,32,16,8,4,2,2,

%e 0,256,128,64,32,16,8,4,2,2,

%e 0,512,256,128,64,32,16,8,4,2,2,

%K nonn,tabl,easy

%O 0,3

%A _Philippe Deléham_, Oct 05 2009