A140883 - OEIS

%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