This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137307 #10 May 06 2025 06:53:24
%S A137307 1,1,-1,1,2,1,-3,-8,4,8,-1,5,18,-20,-48,16,32,1,-7,-32,56,160,-112,
%T A137307 -256,64,128,-1,9,50,-120,-400,432,1120,-576,-1280,256,512,1,-11,-72,
%U A137307 220,840,-1232,-3584,2816,6912,-2816,-6144,1024,2048,-1,13,98,-364,-1568,2912,9408,-9984,-26880,16640,39424,-13312,-28672,4096,8192
%N A137307 A triangular sequence of coefficients of even plus odd Chebyshev polynomials, A053120: q(x,n) = T(x,2*n-1)+T(x,2*n).
%C A137307 The row sums are all 2 and double integrations are all orthogonal except for the zero to one level.
%C A137307 This arose from an idea of Chladni Chebyshev's:
%C A137307 q(exp(i*t),n) = T(cos(2*Pi*t),2*n-1)+T(sin(2*Pi*t),2*n)
%C A137307 which are strange looping spirals.
%F A137307 q(x,n) = T(x,2*n-1)+T(x,2*n).
%e A137307 Triangle begins:
%e A137307 {1, 1},
%e A137307 {-1, 1, 2},
%e A137307 {1, -3, -8, 4, 8},
%e A137307 {-1, 5, 18, -20, -48, 16, 32},
%e A137307 {1, -7, -32, 56, 160, -112, -256, 64, 128},
%e A137307 {-1, 9, 50, -120, -400, 432, 1120, -576, -1280, 256, 512},
%e A137307 {1, -11, -72, 220, 840, -1232, -3584, 2816, 6912, -2816, -6144, 1024, 2048},
%e A137307 {-1, 13, 98, -364, -1568, 2912, 9408, -9984, -26880, 16640, 39424, -13312, -28672, 4096, 8192},
%e A137307 ...
%t A137307 Q[x_, n_] := ChebyshevT[2*n - 1, x] + ChebyshevT[2*n, x]; Table[ExpandAll[Q[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a0]
%Y A137307 Cf. A053120.
%K A137307 uned,tabf,sign
%O A137307 1,5
%A A137307 _Roger L. Bagula_, Apr 20 2008