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 A099044 #16 Sep 08 2022 08:45:15
%S A099044 1,2,18,180,1890,20412,224532,2501928,28146690,318995820,3636552348,
%T A099044 41655054168,479033122932,5527305264600,63958818061800,
%U A099044 741922289516880,8624846615633730,100454095876204620,1171964451889053900,13693479385229998200,160213708807190978940
%N A099044 a(n) = (2*0^n + 3^n*binomial(2*n,n))/3.
%C A099044 (1 + (k-1)*sqrt(1-4*k*x))/(k*sqrt(1-4*k*x)) is the g.f. for ((k-1)*0^n + k^n*binomial(2*n,n))/k.
%H A099044 Vincenzo Librandi, <a href="/A099044/b099044.txt">Table of n, a(n) for n = 0..900</a>
%F A099044 G.f.: 1/3 + 4*x/(sqrt(1-12*x)(1-sqrt(1-12*x))) = (1 + 2*sqrt(1-12*x))/(3*sqrt(1-12*x)).
%F A099044 n*a(n) +6*(-2*n+1)*a(n-1)=0. - _R. J. Mathar_, Nov 24 2012
%F A099044 E.g.f.: (2 + exp(6*x) * BesselI(0,6*x)) / 3. - _Ilya Gutkovskiy_, Nov 17 2021
%t A099044 Join[{1}, Table[3^(n-1)*binomial(2*n,n), {n,1,30}]] (* _G. C. Greubel_, Dec 31 2017 *)
%o A099044 (Magma) [(2*0^n + 3^n*Binomial(2*n, n))/3: n in [ 0..20]]; // _Vincenzo Librandi_, Nov 24 2012
%o A099044 (PARI) for(n=0, 30, print1((2*0^n + 3^n*binomial(2*n,n))/3, ", ")) \\ _G. C. Greubel_, Dec 31 2017
%Y A099044 Cf. A069723, A088218, A099045, A099046.
%K A099044 easy,nonn
%O A099044 0,2
%A A099044 _Paul Barry_, Sep 24 2004