%I A123027
%S A123027 1,2,3,3,10,8,4,22,38,21,5,40,111,130,55,6,65,256,474,420,144,7,98,511,
               1324,
%T A123027 1836,1308,377,8,140,924,3130,6020,6666,3970,987,9,192,1554,6588,16435,
               25088,
%U A123027 23109,11822,2584,10,255,2472,12720,39430,77645,98160,77378,34690,6765,
               11,330
%V A123027 1,-2,3,3,-10,8,-4,22,-38,21,5,-40,111,-130,55,-6,65,-256,474,-420,144,
               7,-98,511,-1324,
%W A123027 1836,-1308,377,-8,140,-924,3130,-6020,6666,-3970,987,9,-192,1554,-6588,
               16435,-25088,
%X A123027 23109,-11822,2584,-10,255,-2472,12720,-39430,77645,-98160,77378,-34690,
               6765,11,-330
%N A123027 A053122(n,m)=CoefficientList(ChebyshevU[n, x/2 - 1]): triangular array 
               made from Bezier transform of A053122.
%C A123027 Alternative Adamson Matrix method: T[n_, m_] = If[ n == m, 2, If[n == 
               m - 1 || n == m + 1, 1, 0]]; M[d_] := Table[T[n, m], {n, 1, d}, {m, 
               1, d}]; Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{1}}, 
               Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 
               10}]]; b = Table[CoefficientList[Sum[a[[m + 1]][[n + 1]]*x^n*(1 - 
               x)^(m - n), {n, 0, m}], x], {m, 0, 10}]; Flatten[b]
%F A123027 T(n,m)=A053122(n,m) T'(n,m)=t(n,m)*x^n*(1-x)^(m-n)
%e A123027 1
%e A123027 -2, 3
%e A123027 3, -10, 8,
%e A123027 -4, 22, 38, 21
%e A123027 5, -40, 111, -130, 55
%t A123027 b0 = Table[CoefficientList[ExpandAll[ChebyshevU[n, x/2 - 1]], x], {n, 
               0, 10}]; c0 = Table[CoefficientList[Sum[b0[[m + 1]][[n + 1]]*x^n*(1 
               - x)^(m - n), {n, 0, m}], x], {m, 0, 10}]; Flatten[c0]
%Y A123027 Cf. A053122.
%Y A123027 Sequence in context: A124931 A124932 A110042 this_sequence A100652 A094416 
               A152300
%Y A123027 Adjacent sequences: A123024 A123025 A123026 this_sequence A123028 A123029 
               A123030
%K A123027 sign,uned,tabl
%O A123027 1,2
%A A123027 Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 24 2006