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%I #3 Mar 30 2012 17:34:23
%S 1,0,1,-2,0,2,0,-7,0,4,8,0,-22,0,8,0,51,0,-64,0,16,-48,0,234,0,-176,0,
%T 32,0,-453,0,916,0,-464,0,64,384,0,-2778,0,3240,0,-1184,0,128,0,4845,
%U 0,-13800,0,10656,0,-2944,0,256,-3840,0,37470,0,-60000,0,33152,0,-7168,0,512
%N Triangle of coefficients of Hermite-like analog of A053120 Chebyshev's T(n, x) polynomials (powers of x in increasing order): p(x,n)=2*x*p(x,n-1)-n*p(x,n-2).
%C Row sums:
%C {1, 1, 0, -3, -6, 3, 42, 63, -210, -987, 126}
%F p(x,n)=2*x*p(x,n-1)-n*p(x,n-2).
%e {1},
%e {0, 1},
%e {-2, 0, 2},
%e {0, -7, 0, 4},
%e {8, 0, -22, 0, 8},
%e {0, 51, 0, -64, 0, 16},
%e {-48, 0, 234, 0, -176, 0, 32},
%e {0, -453, 0, 916, 0, -464,0, 64},
%e {384, 0, -2778, 0, 3240, 0, -1184, 0, 128},
%e {0, 4845, 0, -13800, 0, 10656, 0, -2944, 0,256},
%e {-3840, 0, 37470, 0, -60000, 0, 33152, 0, -7168, 0, 512}
%t P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - n*P[x, n - 2]; Table[ExpandAll[P[x, n]], {n, 0, 10}]; a = Table[CoefficientList[P[x, n], x], {n, 0, 10}]; Flatten[a]
%Y Cf. A053120.
%K uned,tabl,sign
%O 1,4
%A _Roger L. Bagula_, Apr 02 2008
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