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%I #4 Mar 30 2012 18:37:44
%S 1,1,1,1,2,0,1,3,1,-1,1,4,3,-2,0,1,5,6,-2,-2,2,1,6,10,0,-6,4,0,1,7,15,
%T 5,-11,3,5,-5,1,8,21,14,-15,-4,15,-10,0,1,9,28,28,-15,-19,26,-6,-14,
%U 14,1,10,36,48,-7,-42,30,16,-42,28,0,1,11,45,75,14,-70,16,60,-70,14,42,-42,1,12,55,110,54,-96,-28,120,-70,-56,126,-84,0,1
%N Triangle read by rows in which each term equals the entry above minus the entry left plus twice the entry left-above.
%C Row sums are A086990 or A090412. (Superseeker finds that the j-th coefficient of OGF(A090412)(z)*(1-z)^j equals A049122). Same absolute values as A065432. Even rows end in 0, odd rows end in Catalan numbers (A000118) with alternating sign.
%F T(i, j)=T(i-1, j)-T(i, j-1)+2*T(i-1, j-1), with T(i, 0)=1 and T(i, j)=0 if j>i.
%e Table starts {1},{1,1},{1,2,0},{1,3,1,-1},{1,4,3,-2,0},{1,5,6,-2,-2,2}
%t T[_, 0]:=1;T[0, 0]:=1;T[i_, j_]/;j>i:=0;T[i_, j_]:=T[i, j]=T[i-1, j]-T[i, j-1]+2 T[i-1, j-1]
%Y Cf. A086990, A090412, A049122, A009766, A065432, A065441.
%K sign,tabl
%O 0,5
%A _Wouter Meeussen_, May 06 2004
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