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%I #3 Mar 30 2012 17:34:23
%S 1,1,1,0,2,2,-2,0,6,4,-4,-8,4,16,8,-4,-20,-20,20,40,16,0,-24,-72,-40,
%T 72,96,32,8,0,-112,-224,-56,224,224,64,16,64,-32,-448,-624,0,640,512,
%U 128,16,144,288,-288,-1584,-1584,384,1728,1152,256,0,160,800,960,-1600,-5088,-3680,1920,4480,2560,512
%N Triangle of coefficients of the Pascal sum of A053120 Chebyshev's T(n, x) polynomials :p(x,n)=2*x*p(x,n-1)-p(x,n-2); pp(x,n)=Sum[Binomial[n,m]*p(x,m),{m,0,n}].
%C Row sums:
%C {1, 0, -2, -6, -14, -30, -62, -126, -254, -510, -1022}
%F p(x,n)=2*x*p(x,n-1)-p(x,n-2); pp(x,n)=Sum[Binomial[n,m]*p(x,m),{m,0,n}]
%e {1},
%e {1, 1},
%e {0, 2, 2},
%e {-2, 0, 6, 4},
%e {-4, -8, 4, 16, 8},
%e {-4, -20, -20, 20, 40, 16},
%e {0, -24, -72, -40, 72, 96, 32},
%e {8, 0, -112, -224, -56, 224, 224, 64},
%e {16, 64, -32, -448, -624, 0, 640, 512, 128},
%e {16, 144, 288, -288, -1584, -1584, 384, 1728, 1152, 256},
%e {0,160, 800, 960, -1600, -5088, -3680, 1920, 4480, 2560, 512}
%t P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - P[x, n - 2]; Q[x_, n_] := Q[x, n] = Sum[P[x, m]*Binomial[n, m], {m, 0, n}]; a = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a]
%Y Cf. A053120.
%K uned,tabl,sign
%O 1,5
%A _Roger L. Bagula_, Apr 02 2008
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