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%I #6 Feb 22 2013 14:40:24
%S 1,1,1,1,1,0,1,1,-1,-1,1,1,-2,-3,-1,1,1,-3,-5,-2,0,1,1,-4,-7,-2,2,1,1,
%T 1,-5,-9,-1,7,5,1,1,1,-6,-11,1,15,12,3,0,1,1,-7,-13,4,26,21,3,-3,-1,1,
%U 1,-8,-15,8,40,31,-3,-15,-7,-1
%N Triangle T(n,k), read by rows, given by (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
%C Mirror image of triangle in A129267.
%F T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) - T(n-2,l-2) with T(0,0)= T(1,0) = T(1,1) = 1 and T(n,k) = 0 if k<0 or if n<k.
%F Sum_{k, 0<=k<=n} T(n,k)*x^k = A000012(n), A099087(n), A190960(n+1) for x = 0, 1, 2 respectively.
%F G.f.: 1/(1-(1+y)*x+(y+y^2)*x^2).
%e Triangle begins :
%e 1
%e 1, 1
%e 1, 1, 0
%e 1, 1, -1, -1
%e 1, 1, -2, -3, -1
%e 1, 1, -3, -5, -2, 0
%e 1, 1, -4, -7, -2, 2, 1
%e 1, 1, -5, -9, -1, 7, 5, 1
%Y Cf. A129267, A010892, A005449
%K sign,tabl
%O 0,13
%A _Philippe Deléham_, Dec 21 2011
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