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A123966 Triangle A124029 with the (0,0) entry replaced by 4.

%I A123966 #12 Aug 09 2015 01:19:52
%S A123966 4,4,-1,15,-8,1,56,-46,12,-1,209,-232,93,-16,1,780,-1091,592,-156,20,
%T A123966 -1,2911,-4912,3366,-1200,235,-24,1,10864,-21468,17784,-8010,2120,
%U A123966 -330,28,-1,40545,-91824,89238,-48624,16255,-3416,441,-32,1,151316,-386373,430992,-275724,111524,-29589,5152,-568,36
%N A123966 Triangle A124029 with the (0,0) entry replaced by 4.
%C A123966 The entry for the empty matrix in row 0 and column 0 is replaced by 4 in comparison to the variant in A124029.
%e A123966 4;
%e A123966 4, -1;
%e A123966 15, -8, 1;
%e A123966 56, -46,12, -1;
%e A123966 209, -232, 93, -16, 1;
%e A123966 780, -1091, 592, -156, 20, -1;
%e A123966 2911, -4912, 3366, -1200, 235, -24, 1;
%e A123966 10864, -21468, 17784, -8010, 2120, -330, 28, -1;
%t A123966 Clear[M, T, d, a, x]; T[n_, m_] = If[ n == m, 4, If[n == m - 1 || n == m + 1, -1, 0]]; M[d_] := Table[T[n, m], {n, 1, d}, {m, 1, d}]; Table[M[d], {d, 1, 10}]; Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{3}}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a]
%Y A123966 Cf. A123343, A159764.
%K A123966 tabl,sign
%O A123966 0,1
%A A123966 _Gary W. Adamson_ and _Roger L. Bagula_, Oct 28 2006