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%I #6 Sep 12 2013 15:53:56
%S 2,1,1,1,0,1,4,-3,-3,4,9,0,-16,0,9,16,5,-20,-20,5,16,31,0,-30,0,-30,0,
%T 31,64,-7,-112,56,56,-112,-7,64,129,0,-288,0,320,0,-288,0,129,256,9,
%U -576,-120,432,432,-120,-576,9,256,511,0,-1230,0,720,0,720,0,-1230,0,511
%N Triangle T(n,k) = A053120(n,k)+A053120(n,n-k) of symmetrized Chebyshev coefficients, read by rows, 0<=k<=n.
%C Row sums are constantly two.
%F T(n,k) = T(n,n-k).
%e 2;
%e 1, 1;
%e 1, 0, 1;
%e 4, -3, -3, 4;
%e 9, 0, -16, 0, 9;
%e 16, 5, -20, -20, 5, 16;
%e 31, 0, -30, 0, -30, 0, 31;
%e 64, -7, -112, 56, 56, -112, -7, 64;
%e 129, 0, -288, 0, 320, 0, -288, 0, 129;
%e 256, 9, -576, -120, 432, 432, -120, -576, 9, 256;
%e 511, 0, -1230, 0, 720, 0, 720, 0, -1230, 0, 511;
%t Clear[p, x, n, m, a]; p[x_, n_] := ChebyshevT[n, x] + ExpandAll[x^n*ChebyshevT[n, 1/x]]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]
%Y Cf. A053120.
%K tabl,sign
%O 0,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Jul 22 2008
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