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Array read by antidiagonals of signed variant of trinomial coefficients with T(n,k)=T(n-1,k)+T(n-1,k-1)-T(n-1,k-2) starting with T(0,0)=1.
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%I #5 Mar 10 2018 05:37:43

%S 1,0,1,0,1,1,0,-1,2,1,0,0,-1,3,1,0,0,-2,0,4,1,0,0,1,-5,2,5,1,0,0,0,0,

%T -8,5,6,1,0,0,0,3,-5,-10,9,7,1,0,0,0,-1,8,-15,-10,14,8,1,0,0,0,0,2,11,

%U -30,-7,20,9,1,0,0,0,0,-4,15,6,-49,0,27,10,1,0,0,0,0,1,-10,41,-14,-70,12,35,11,1,0,0,0,0,0,-5,-6,77,-56,-90,30,44

%N Array read by antidiagonals of signed variant of trinomial coefficients with T(n,k)=T(n-1,k)+T(n-1,k-1)-T(n-1,k-2) starting with T(0,0)=1.

%C Each column is eventually positive, i.e. for each k there is a number j(k) such that T(n,k) is positive for all n>=j(k). Despite this, each row sum is 1.

%e Rows start:

%e 1, 0, 0, 0, 0, ...;

%e 1, 1, -1, 0, 0, 0, ...;

%e 1, 2, -1, -2, 1, 0, 0, ...;

%e 1, 3, 0, -5, 0, 3, -1, 0, ...;

%e 1, 4, 2, -8, -5, 8, 2, -4, 1, ...;

%e etc...

%Y Cf. A071675.

%K sign,tabl

%O 0,9

%A _Henry Bottomley_, May 30 2002