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A140883
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Triangle T(n,k) = A053120(n,k)+A053120(n,n-k) of symmetrized Chebyshev coefficients, read by rows, 0<=k<=n.
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0
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2, 1, 1, 1, 0, 1, 4, -3, -3, 4, 9, 0, -16, 0, 9, 16, 5, -20, -20, 5, 16, 31, 0, -30, 0, -30, 0, 31, 64, -7, -112, 56, 56, -112, -7, 64, 129, 0, -288, 0, 320, 0, -288, 0, 129, 256, 9, -576, -120, 432, 432, -120, -576, 9, 256, 511, 0, -1230, 0, 720, 0, 720, 0, -1230, 0, 511
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OFFSET
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0,1
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COMMENTS
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Row sums are constantly two.
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LINKS
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FORMULA
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T(n,k) = T(n,n-k).
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EXAMPLE
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2;
1, 1;
1, 0, 1;
4, -3, -3, 4;
9, 0, -16, 0, 9;
16, 5, -20, -20, 5, 16;
31, 0, -30, 0, -30, 0, 31;
64, -7, -112, 56, 56, -112, -7, 64;
129, 0, -288, 0, 320, 0, -288, 0, 129;
256, 9, -576, -120, 432, 432, -120, -576, 9, 256;
511, 0, -1230, 0, 720, 0, 720, 0, -1230, 0, 511;
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MATHEMATICA
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Clear[p, x, n, m, a]; p[x_, n_] := ChebyshevT[n, x] + ExpandAll[x^n*ChebyshevT[n, 1/x]]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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