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 A119575 #18 Oct 23 2023 12:28:00
%S A119575 9,16,50,180,686,2688,10692,42900,173030,700128,2838524,11522056,
%T A119575 46802700,190182400,772913160,3141129780,12764118870,51857916000,
%U A119575 210638666700,855355383960,3472419702180,14092569803520,57176602275000,231908298827400,940340123399196,3811765978738368
%N A119575 a(n) = binomial(2*n,n)*(n+3)^2/(n+1).
%F A119575 From _Stefano Spezia_, Aug 24 2023: (Start)
%F A119575 O.g.f.: (2*(sqrt(1 - 4*x) - 1) + x*(21 - 8*sqrt(1 - 4*x) - 50*x))/(x*(1 - 4*x)^(3/2)).
%F A119575 E.g.f.: exp(2*x)*((9 + 2*x)*BesselI(0, 2*x) + 2*(x - 2)*BesselI(1, 2*x)).
%F A119575 a(n) ~ c*4^n*sqrt(n), where c = A087197. (End)
%p A119575 [seq (binomial(2*n,n)*(n+3)^2/(n+1),n=0..25)];
%t A119575 a[n_] := Binomial[2*n, n]*(n + 3)^2/(n + 1); Table[a[n], {n, 0, 25}] (* _Robert P. P. McKone_, Aug 25 2023 *)
%o A119575 (PARI) a(n) = binomial(2*n,n)/(n+1)*(n+3)^2 \\ _Charles R Greathouse IV_, Oct 23 2023
%Y A119575 Cf. A000984, A087197.
%K A119575 easy,nonn
%O A119575 0,1
%A A119575 _Zerinvary Lajos_, May 31 2006
%E A119575 More terms from _Stefano Spezia_, Aug 24 2023