This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317405 #59 Feb 16 2025 08:33:56
%S A317405 1,8,45,224,1045,4680,20377,86912,364905,1513160,6211909,25290720,
%T A317405 102251773,410963336,1643288625,6541692416,25939798993,102503274120,
%U A317405 403800061789,1586318259680,6216231359205,24304019419592,94826736906697,369285078314880,1435615286196025
%N A317405 a(n) = n * A001353(n).
%C A317405 Derivative of Chebyshev polynomials of the first kind evaluated at x=2.
%H A317405 Colin Barker, <a href="/A317405/b317405.txt">Table of n, a(n) for n = 1..1000</a>
%H A317405 Rigoberto Flórez, Robinson Higuita, and Alexander Ramírez, <a href="https://arxiv.org/abs/1808.01264"> The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials</a>, arXiv:1808.01264 [math.NT], 2018.
%H A317405 Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Florez2/florez8.html">Star of David and other patterns in the Hosoya-like polynomials triangles</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.4.6.
%H A317405 R. Flórez, N. McAnally, and A. Mukherjees, <a href="http://math.colgate.edu/~integers/s18b2/s18b2.Abstract.html">Identities for the generalized Fibonacci polynomial</a>, Integers, 18B (2018), Paper No. A2.
%H A317405 R. Flórez, R. Higuita and A. Mukherjees, <a href="http://math.colgate.edu/~integers/s14/s14.Abstract.html">Characterization of the strong divisibility property for generalized Fibonacci polynomials</a>, Integers, 18 (2018), Paper No. A14.
%H A317405 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html">Chebyshev Polynomial of the First Kind</a>
%H A317405 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-18,8,-1).
%F A317405 From _Colin Barker_, Jul 28 2018: (Start)
%F A317405 G.f.: x*(1 - x)*(1 + x) / (1 - 4*x + x^2)^2.
%F A317405 a(n) = (((-(2-sqrt(3))^n + (2+sqrt(3))^n)*n)) / (2*sqrt(3)).
%F A317405 a(n) = 8*a(n-1) - 18*a(n-2) + 8*a(n-3) - a(n-4) for n>4.
%F A317405 (End)
%t A317405 Table[ D[ ChebyshevT[n, x], x] /. x -> 2, {n, 25}]
%t A317405 CoefficientList[Series[-x(x^2 - 1)/(x^2 - 4x + 1)^2, {x, 0, 24}], x] (* _Robert G. Wilson v_, Aug 07 2018 *)
%o A317405 (PARI) Vec(x*(1 - x)*(1 + x) / (1 - 4*x + x^2)^2 + O(x^40)) \\ _Colin Barker_, Jul 28 2018
%o A317405 (PARI) a(n) = subst(deriv(polchebyshev(n)), x, 2); \\ _Michel Marcus_, Jul 29 2018
%Y A317405 Cf. A001353, A028297 (Chebyshev polynomials of the first kind).
%K A317405 nonn,easy
%O A317405 1,2
%A A317405 _Rigoberto Florez_, Jul 27 2018