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A100551
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Coefficient list of ChebyshevU(n, 1-x).
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2
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1, 2, -2, 3, -8, 4, 4, -20, 24, -8, 5, -40, 84, -64, 16, 6, -70, 224, -288, 160, -32, 7, -112, 504, -960, 880, -384, 64, 8, -168, 1008, -2640, 3520, -2496, 896, -128, 9, -240, 1848, -6336, 11440, -11648, 6720, -2048, 256, 10, -330, 3168, -13728, 32032, -43680, 35840, -17408, 4608, -512
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: ChebyshevU(n, 1-x).
T(n, k) = binomial(n+k+1, n-k)*(-2)^k.
T(n, n-1) = 2*(-1)^(n-1)*A001787(n), n >= 1.
Sum_{k=0..n} (-1)^k*T(n, k) = A001353(n+1). (End)
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EXAMPLE
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Triangle begins as:
1;
2, -2;
3, -8, 4;
4, -20, 24, -8;
5, -40, 84, -64, 16;
6, -70, 224, -288, 160, -32;
7, -112, 504, -960, 880, -384, 64;
8, -168, 1008, -2640, 3520, -2496, 896, -128;
9, -240, 1848, -6336, 11440, -11648, 6720, -2048, 256;
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MATHEMATICA
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Table[CoefficientList[ChebyshevU[n, 1-x], x], {n, 0, 12}]
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PROG
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(PARI) row(n) = Vecrev(polchebyshev(n, 2, 1-x)); \\ Michel Marcus, Apr 27 2020
(Magma) [Binomial(n+k+1, n-k)*(-2)^k: k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 27 2023
(SageMath)
def A100551(n, k): return binomial(n+k+1, n-k)*(-2)^k
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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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