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%I #14 Jul 23 2017 03:14:24
%S 1,1,-1,1,0,0,1,0,-1,0,1,0,0,0,0,1,0,0,-1,0,0,1,0,0,0,0,0,0,1,0,0,0,
%T -1,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%U 0,1,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,0
%N Weight array of A185914, by antidiagonals.
%C A member of the accumulation chain ... < A185916 < A185914 < A185915 < ...
%C (See A144112 for definitions of weight array and accumulation array.)
%H G. C. Greubel, <a href="/A185916/b185916.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F T(1,k)=1 for k>=1; T(n,n+1)=-1 for n>=2; T(n,k)=0 otherwise; for k>=1, n>=1.
%e Northwest corner:
%e 1, 1, 1, 1, 1, 1, 1
%e -1, 0, 0, 0, 0, 0, 0
%e 0, -1, 0, 0, 0, 0, 0
%e 0, 0, -1, 0, 0, 0, 0
%e 0, 0, 0, -1, 0, 0, 0
%e 0, 0, 0, 0, -1, 0, 0
%t f[n_, 0] := 0; f[0, k_] := 0; f[n_, k_] := k - n + 1; f[n_, k_] := 0 /; k < n; w[m_, n_] := f[m, n] + f[m - 1, n - 1] - f[m, n - 1] - f[m - 1, n] /; Or[m > 0, n > 0]; Table[w[n - k + 1, k], {n, 50}, {k, n, 1, -1}] // Flatten
%Y Cf. A115359, A144112, A185914, A185915.
%K tabl,sign
%O 1
%A _Clark Kimberling_, Feb 06 2011
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