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 A126952 #19 Jun 22 2025 06:34:12
%S A126952 1,1,5,21,93,421,1937,9017,42349,200277,952425,4549953,21818841,
%T A126952 104966889,506372277,2448641061,11865563853,57604036309,280110716777,
%U A126952 1364092539041,6651682319233,32474171399649,158714415664557
%N A126952 a(0)=1, a(n+1) = 5*a(n)-4*A117641(n) for n>=0.
%C A126952 Hankel transform is 4^n=A000302(n).
%H A126952 Michael De Vlieger, <a href="/A126952/b126952.txt">Table of n, a(n) for n = 0..1001</a>
%H A126952 Isaac DeJager, Madeleine Naquin, Frank Seidl, <a href="https://www.valpo.edu/mathematics-statistics/files/2019/08/Drube2019.pdf">Colored Motzkin Paths of Higher Order</a>, VERUM 2019.
%F A126952 a(n) = Sum_{k = 0..n} binomial(n,k)*b(k), where b(n) = Sum_{k = 0..n} binomial(n+k,k) * (-2)^(n-k). - _Peter Bala_, Jun 18 2025
%F A126952 From _Vaclav Kotesovec_, Jun 22 2025: (Start)
%F A126952 Recurrence: 5*(n-2)*a(n-3) + (9*n-26)*a(n-2) + (12-17*n)*a(n-1) + 3*n*a(n) = 0.
%F A126952 a(n) ~ 5^(n + 1/2) / (4*sqrt(Pi*n)). (End)
%t A126952 Block[{$MaxExtraPrecision = 10^3, s = Rest@ CoefficientList[Series[(1 + 3 x - Sqrt[1 - 6 x + 5 x^2])/(2 x^2 + 6 x), {x, 0, 21}], x]}, Nest[Append[#, 5 #[[-1]] - 4 s[[Length@ # - 1]] ] &, {1, 1}, Length@ s]] (* _Michael De Vlieger_, Dec 15 2019, after _Robert G. Wilson v_ at A117641 *)
%Y A126952 Cf. A000302, A117641.
%K A126952 nonn
%O A126952 0,3
%A A126952 _Philippe Deléham_, Mar 19 2007
%E A126952 a(11) and a(22) corrected by _Michael De Vlieger_, Dec 15 2019