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%I #3 Mar 30 2012 17:34:26
%S 1,1,1,0,1,2,0,-2,2,4,1,-2,-6,4,8,1,3,-6,-16,8,16,0,3,12,-16,-40,16,
%T 32,0,-4,12,40,-40,-96,32,64,1,-4,-20,40,120,-96,-224,64,128,1,5,-20,
%U -80,120,336,-224,-512,128,256,0,5,30,-80,-280,336,896,-512,-1152,256,512
%N Triangular sequence from coefficients of a cumulative sum of Chebyshev T(x,n) polynomials (A053120): p(x,n)=p(x,n-1)+T(x,n).
%C Row sums are: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
%F p(x,n)=p(x,n-1)+T(x,n); out_n,m=Coefficients(p(x,n)).
%e {1},
%e {1, 1},
%e {0, 1, 2},
%e {0, -2, 2, 4},
%e {1, -2, -6, 4, 8},
%e {1, 3, -6, -16, 8, 6},
%e {0, 3, 12, -16, -40, 16, 32},
%e {0, -4, 12, 40, -40, -96, 32, 64},
%e {1, -4, -20, 40, 120, -96, -224, 64, 128},
%e {1, 5, -20, -80, 120, 336, -224, -512, 128, 256},
%e {0, 5, 30, -80, -280, 336,896, -512, -1152, 256, 512}
%t Clear[P] P[x, -1] = 0; P[x, 0] = 1; P[x_, n_] := P[x, n] = P[x, n - 1] + ChebyshevT[n, 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 1,6
%A _Roger L. Bagula_, Apr 27 2008
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