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 A100551 Coefficient list of ChebyshevU(n, 1-x). 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened Index entries for sequences related to Chebyshev polynomials. FORMULA G.f.: ChebyshevU(n, 1-x). From G. C. Greubel, Mar 27 2023: (Start) T(n, k) = binomial(n+k+1, n-k)*(-2)^k. T(n, n) = A122803(n). T(n, n-1) = 2*(-1)^(n-1)*A001787(n), n >= 1. Sum_{k=0..n} T(n, k) = A056594(n). Sum_{k=0..n} (-1)^k*T(n, k) = A001353(n+1). (End) EXAMPLE 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; MATHEMATICA Table[CoefficientList[ChebyshevU[n, 1-x], x], {n, 0, 12}] PROG (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 flatten([[A100551(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Mar 27 2023 CROSSREFS Cf. A001353, A001787, A053117, A056594, A122803. Sequence in context: A238654 A220553 A176383 * A267667 A210190 A070267 Adjacent sequences: A100548 A100549 A100550 * A100552 A100553 A100554 KEYWORD easy,sign,tabl AUTHOR Wouter Meeussen, Nov 27 2004 EXTENSIONS Keyword tabl from Michel Marcus, Apr 27 2020 STATUS approved

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Last modified June 14 04:49 EDT 2024. Contains 373393 sequences. (Running on oeis4.)