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 A098444 #25 Jan 30 2020 21:29:15
%S A098444 1,3,19,117,771,5193,35629,247467,1734931,12250953,87006249,620818047,
%T A098444 4447016781,31959556983,230331965379,1664043517557,12047551338771,
%U A098444 87387014213433,634918255153369,4619923954541247,33661450900419001
%N A098444 Expansion of 1/sqrt(1-6x-11x^2).
%C A098444 Binomial transform of A084770. Second binomial transform of A098264. Binomial transform is A098443.
%C A098444 Coefficient of x^n in (1 + 3 x + 5 x^2)^n = number of paths from the origin to (n,0) with steps U=(1,1), H=(1,0) and D=(1,-1); U can have 5 colors and H can have 3 colors. - _N-E. Fahssi_, Jan 28 2008
%H A098444 Vincenzo Librandi, <a href="/A098444/b098444.txt">Table of n, a(n) for n = 0..200</a>
%H A098444 Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Szalay/szalay42.html">Diagonal Sums in the Pascal Pyramid, II: Applications</a>, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
%H A098444 Tony D. Noe, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html">On the Divisibility of Generalized Central Trinomial Coefficients</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%F A098444 E.g.f.: exp(3x)*BesselI(0, 2*sqrt(5)*x)
%F A098444 D-finite with recurrence: n*a(n) = 3*(2*n-1)*a(n-1) + 11*(n-1)*a(n-2). - _Vaclav Kotesovec_, Oct 15 2012
%F A098444 a(n) ~ sqrt(50+15*sqrt(5))*(3+2*sqrt(5))^n/(10*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 15 2012
%t A098444 Table[SeriesCoefficient[1/Sqrt[1-6*x-11*x^2],{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 15 2012 *)
%o A098444 (PARI) x='x+O('x^66); Vec(1/sqrt(1-6*x-11*x^2)) \\ _Joerg Arndt_, May 11 2013
%K A098444 easy,nonn
%O A098444 0,2
%A A098444 _Paul Barry_, Sep 07 2004