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%I #2 Mar 30 2012 17:34:33
%S -2,-3,8,-3,-6,10,10,-6,-17,16,24,16,-17,-30,4,52,52,4,-30,-63,24,56,
%T 80,56,24,-63,-126,22,234,-10,-10,234,22,-126,-257,32,488,224,-480,
%U 224,488,32,-257,-510,8,1096,328,-420,-420,328,1096,8,-510,-1023,40,2244,480
%N A triangle of polynomial coefficients: p(x,n)=-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n)); sp(x,n) = p(x, n) + x^n*p(1/x, n).
%C Row sums are:
%C {-2, 0, 2, 8, 22, 52, 114, 240, 494, 1004, 2026,...}.
%F p(x,n)=-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n));
%F sp(x,n) = p(x, n) + x^n*p(1/x, n).
%e {-2},
%e {},
%e {-3, 8, -3},
%e {-6, 10, 10, -6},
%e {-17, 16, 24, 16, -17},
%e {-30, 4, 52, 52, 4, -30},
%e {-63, 24, 56, 80, 56, 24, -63},
%e {-126, 22, 234, -10, -10, 234, 22, -126},
%e {-257, 32, 488, 224, -480, 224, 488, 32, -257},
%e {-510, 8, 1096, 328, -420, -420, 328, 1096, 8, -510},
%e {-1023, 40, 2244, 480, -1232, 1008, -1232, 480, 2244, 40, -1023}
%t p[x_, n_] =-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n));
%t sp[x_, n_] = p[x, n] + x^n*p[1/x, n];
%t Table[FullSimplify[ExpandAll[sp[x, n]]], {n, 0, 10}];
%t Table[CoefficientList[FullSimplify[ExpandAll[sp[x, n]]], x], {n, 0, 10}]; Q Flatten[%]
%K sign,tabl,uned
%O 0,1
%A _Roger L. Bagula_, Feb 01 2009
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