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A317405
a(n) = n * A001353(n).
5
1, 8, 45, 224, 1045, 4680, 20377, 86912, 364905, 1513160, 6211909, 25290720, 102251773, 410963336, 1643288625, 6541692416, 25939798993, 102503274120, 403800061789, 1586318259680, 6216231359205, 24304019419592, 94826736906697, 369285078314880, 1435615286196025
OFFSET
1,2
COMMENTS
Derivative of Chebyshev polynomials of the first kind evaluated at x=2.
LINKS
Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, Star of David and other patterns in the Hosoya-like polynomials triangles, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
R. Flórez, N. McAnally, and A. Mukherjees, Identities for the generalized Fibonacci polynomial, Integers, 18B (2018), Paper No. A2.
R. Flórez, R. Higuita and A. Mukherjees, Characterization of the strong divisibility property for generalized Fibonacci polynomials, Integers, 18 (2018), Paper No. A14.
Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind
FORMULA
From Colin Barker, Jul 28 2018: (Start)
G.f.: x*(1 - x)*(1 + x) / (1 - 4*x + x^2)^2.
a(n) = (((-(2-sqrt(3))^n + (2+sqrt(3))^n)*n)) / (2*sqrt(3)).
a(n) = 8*a(n-1) - 18*a(n-2) + 8*a(n-3) - a(n-4) for n>4.
(End)
MATHEMATICA
Table[ D[ ChebyshevT[n, x], x] /. x -> 2, {n, 25}]
CoefficientList[Series[-x(x^2 - 1)/(x^2 - 4x + 1)^2, {x, 0, 24}], x] (* Robert G. Wilson v, Aug 07 2018 *)
PROG
(PARI) Vec(x*(1 - x)*(1 + x) / (1 - 4*x + x^2)^2 + O(x^40)) \\ Colin Barker, Jul 28 2018
(PARI) a(n) = subst(deriv(polchebyshev(n)), x, 2); \\ Michel Marcus, Jul 29 2018
CROSSREFS
Cf. A001353, A028297 (Chebyshev polynomials of the first kind).
Sequence in context: A016208 A216540 A026852 * A110609 A201190 A297089
KEYWORD
nonn,easy
AUTHOR
Rigoberto Florez, Jul 27 2018
STATUS
approved