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 A089927 #29 Aug 25 2024 18:44:56
%S A089927 1,5,25,120,576,2760,13225,63365,303601,1454640,6969600,33393360,
%T A089927 159997201,766592645,3672966025,17598237480,84318221376,403992869400,
%U A089927 1935646125625,9274237758725,44435542668001,212903475581280
%N A089927 Expansion of 1/((1-x^2)(1-5x+x^2)).
%H A089927 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.
%H A089927 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,0,-5,1).
%F A089927 a(n) = 5*a(n-1) - 5*a(n-3) + a(n-4).
%F A089927 a(n) = ((5-sqrt(21))^n*(23 - 5*sqrt(21)) + (5 + sqrt(21))^n*(23 + 5*sqrt(21)))/42/2^n + (-1)^n/14 - 1/6. [corrected by _Jason Yuen_, Aug 25 2024]
%F A089927 a(n) = Sum_{k=0..floor(n/2)} U(n-2k, 5/2) where U is the Chebyshev polynomial of the second kind.
%F A089927 a(n) = (-1)^n/14 - 1/6 + (23*A004254(n+1) - 5*A004254(n))/21. - _R. J. Mathar_, Mar 22 2011
%t A089927 CoefficientList[Series[1/((1-x^2)(1-5x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{5,0,-5,1},{1,5,25,120},30] (* _Harvey P. Dale_, Apr 12 2015 *)
%Y A089927 Cf. A003690, A003769.
%K A089927 easy,nonn
%O A089927 0,2
%A A089927 _Paul Barry_, Nov 15 2003