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%I #14 Mar 27 2023 05:16:33
%S 1,2,-2,3,-8,4,4,-20,24,-8,5,-40,84,-64,16,6,-70,224,-288,160,-32,7,
%T -112,504,-960,880,-384,64,8,-168,1008,-2640,3520,-2496,896,-128,9,
%U -240,1848,-6336,11440,-11648,6720,-2048,256,10,-330,3168,-13728,32032,-43680,35840,-17408,4608,-512
%N Coefficient list of ChebyshevU(n, 1-x).
%H G. C. Greubel, <a href="/A100551/b100551.txt">Rows n = 0..50 of the triangle, flattened</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F G.f.: ChebyshevU(n, 1-x).
%F From _G. C. Greubel_, Mar 27 2023: (Start)
%F T(n, k) = binomial(n+k+1, n-k)*(-2)^k.
%F T(n, n) = A122803(n).
%F T(n, n-1) = 2*(-1)^(n-1)*A001787(n), n >= 1.
%F Sum_{k=0..n} T(n, k) = A056594(n).
%F Sum_{k=0..n} (-1)^k*T(n, k) = A001353(n+1). (End)
%e Triangle begins as:
%e 1;
%e 2, -2;
%e 3, -8, 4;
%e 4, -20, 24, -8;
%e 5, -40, 84, -64, 16;
%e 6, -70, 224, -288, 160, -32;
%e 7, -112, 504, -960, 880, -384, 64;
%e 8, -168, 1008, -2640, 3520, -2496, 896, -128;
%e 9, -240, 1848, -6336, 11440, -11648, 6720, -2048, 256;
%t Table[CoefficientList[ChebyshevU[n, 1-x], x], {n, 0, 12}]
%o (PARI) row(n) = Vecrev(polchebyshev(n, 2, 1-x)); \\ _Michel Marcus_, Apr 27 2020
%o (Magma) [Binomial(n+k+1, n-k)*(-2)^k: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 27 2023
%o (SageMath)
%o def A100551(n,k): return binomial(n+k+1, n-k)*(-2)^k
%o flatten([[A100551(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Mar 27 2023
%Y Cf. A001353, A001787, A053117, A056594, A122803.
%K easy,sign,tabl
%O 0,2
%A _Wouter Meeussen_, Nov 27 2004
%E Keyword tabl from _Michel Marcus_, Apr 27 2020
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