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%I #14 Mar 30 2012 18:52:06
%S 1,2,0,2,0,-1,2,0,-3,0,2,0,-5,0,1,2,0,-7,0,4,0,2,0,-9,0,9,0,-1,2,0,
%T -11,0,16,0,-5,0,2,0,-13,0,25,0,-14,0,1,2,0,-15,0,36,0,-30,0,6,0,2,0,
%U -17,0,49,0,-55,0,20,0,-1
%N Triangle T(n,0) = A040000(n), T(n,k)=0 (odd-numbered columns); T(n,k) = (-1)^(k/2)*A110813(n-k/2-1,k/2-1) (even-numbered columns, k>0).
%C A zero-padded variant of A110813, which provides more information.
%F T(n,k) = T(n-1,k)-T(n-2,k-2), n>1.
%F T(n,2k+1)=0.
%F T(n,2k) = (-1)^k*binomial(n-k-1,k-1)*(2n-3k)/k , k>0. - R. J. Mathar, Aug 26 2011
%F T(n,0) = A040000(n).
%F sum_{k=0..n} T(n,k) = A057079(n).
%F sum_{k=0..n} |T(n,k)| = A000045(n+2). (See A129710).
%e 1;
%e 2 0;
%e 2 0 -1;
%e 2 0 -3 0;
%e 2 0 -5 0 1;
%e 2 0 -7 0 4 0;
%e 2 0 -9 0 9 0 -1;
%e 2 0 -11 0 16 0 -5 0;
%e 2 0 -13 0 25 0 -14 0 1;
%e 2 0 -15 0 36 0 -30 0 6 0;
%Y Cf. A191662.
%K sign,tabl,easy
%O 0,2
%A _Paul Curtz_, Jul 04 2011
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