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 A144139 #23 Aug 04 2025 10:27:46
%S A144139 1,5,209,1189,3905,9701,20305,37829,64769,104005,158801,232805,330049,
%T A144139 454949,612305,807301,1045505,1332869,1675729,2080805,2555201,3106405,
%U A144139 3742289,4471109,5301505,6242501,7303505,8494309,9825089,11306405
%N A144139 Chebyshev polynomial of the second kind U(4,n).
%H A144139 Vincenzo Librandi, <a href="/A144139/b144139.txt">Table of n, a(n) for n = 0..1000</a>
%H A144139 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A144139 G.f.: (1 + 194*x^2 + 184*x^3 + 5*x^4)/(1 - x)^5. - _Vincenzo Librandi_, May 29 2014
%F A144139 a(n) = 16*n^4-12*n^2+1 = (4*n^2-2*n-1)*(4*n^2+2*n-1). - _Vincenzo Librandi_, May 29 2014
%F A144139 From _Klaus Purath_, Sep 08 2022: (Start)
%F A144139 a(n) = A165900(2*n)*A165900(2*n+1).
%F A144139 a(n) = A057722(2*n).
%F A144139 a(n) = 4*(Sum_{i=1..n} A193250(i)) + 1 = 4*A079414(n) + 1.
%F A144139 (End)
%F A144139 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Wesley Ivan Hurt_, Aug 04 2025
%t A144139 lst={}; Do[AppendTo[lst, ChebyshevU[4, n]], {n, 0, 9^2}]; lst
%t A144139 CoefficientList[Series[(1 + 194 x^2 + 184 x^3 + 5 x^4)/(1 - x)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 29 2014 *)
%o A144139 (Magma) [16*n^4-12*n^2+1: n in [0..40]]; // _Vincenzo Librandi_, May 29 2014
%Y A144139 Cf. A057722, A079414, A165900, A193250.
%K A144139 nonn,easy
%O A144139 0,2
%A A144139 _Vladimir Joseph Stephan Orlovsky_, Sep 11 2008
%E A144139 Changed offset from 1 to 0 by _Vincenzo Librandi_, May 29 2014