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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
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
Sequence in context: A238654 A220553 A176383 * A267667 A210190 A070267
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.)