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A137422
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Triangle T(n,k) = A053120(n-1,k) + A053120(n-1,k-1), read by rows.
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1
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0, 1, 1, 0, 1, 1, -1, -1, 2, 2, 0, -3, -3, 4, 4, 1, 1, -8, -8, 8, 8, 0, 5, 5, -20, -20, 16, 16, -1, -1, 18, 18, -48, -48, 32, 32, 0, -7, -7, 56, 56, -112, -112, 64, 64, 1, 1, -32, -32, 160, 160, -256, -256, 128, 128, 0, 9, 9, -120, -120, 432, 432, -576, -576, 256, 256
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OFFSET
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0,9
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COMMENTS
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Row sums are 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
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LINKS
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EXAMPLE
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Triangle begins
0;
1, 1;
0, 1, 1;
-1, -1, 2, 2;
0, -3, -3, 4, 4;
1, 1, -8, -8, 8, 8;
0, 5, 5, -20, -20, 16, 16;
-1, -1, 18, 18, -48, -48, 32, 32;
0, -7, -7, 56, 56, -112, -112, 64, 64;
1, 1, -32, -32, 160, 160, -256, -256, 128, 128;
0, 9, 9, -120, -120, 432, 432, -576, -576, 256, 256;
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MAPLE
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if n <0 or k <0 then
0 ;
else
T(n, x) ;
coeftayl(%, x=0, k) ;
end if;
end proc:
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MATHEMATICA
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(* Chebyshev A053120 polynomials*) (* Recursive root shifted polynomials*) Q[x, 0] = 1; Q[x, 1] = x + 1; Q[x_, n_] := (x + 1)*ChebyshevT[n - 1, x]; Table[ExpandAll[Q[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a0]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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