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%I #2 Mar 30 2012 17:34:33
%S 2,1,1,3,0,3,-2,9,9,-2,-5,0,40,0,-5,-14,5,40,40,5,-14,-27,0,90,0,90,0,
%T -27,-62,21,154,14,14,154,21,-62,-125,0,400,0,-40,0,400,0,-125,-254,9,
%U 648,288,-180,-180,288,648,9,-254,-507,0,1410,0,120,0,120,0,1410,0,-507
%N A triangle of polynomial coefficients: p(x,n)=-(ChebyshevT[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, 2, 6, 14, 30, 62, 126, 254, 510, 1022, 2046,...}.
%F p(x,n)=-(ChebyshevT[n, x] - ((x + 1)^n + (1 - x)^n));
%F sp(x,n) = p(x, n) + x^n*p(1/x, n).
%e {2},
%e {1, 1},
%e {3, 0, 3},
%e {-2, 9, 9, -2},
%e {-5, 0, 40, 0, -5},
%e {-14, 5, 40, 40, 5, -14},
%e {-27, 0, 90, 0, 90, 0, -27},
%e {-62, 21, 154, 14, 14, 154, 21, -62},
%e {-125, 0, 400, 0, -40, 0, 400, 0, -125},
%e {-254, 9, 648, 288, -180, -180, 288, 648, 9, -254},
%e {-507, 0, 1410, 0, 120, 0, 120, 0, 1410, 0, -507}
%t p[x_, n_] = -(ChebyshevT[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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