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 A228484 #31 Feb 26 2025 08:54:00
%S A228484 1,6,60,672,7920,96096,1188096,14883840,188280576,2399654400,
%T A228484 30766095360,396363202560,5126871859200,66538909237248,
%U A228484 866061993246720,11300615801536512,147773778404769792,1936073567335219200,25408660721789829120,333963051307735449600
%N A228484 a(n) = 2^n*(3*n)!/(n!*(2*n)!).
%C A228484 Oblique diagonal of the Pell-Jacobsthal triangle A013609. Its mirror diagonal is A006588.
%H A228484 Vincenzo Librandi, <a href="/A228484/b228484.txt">Table of n, a(n) for n = 0..200</a>
%F A228484 a(n) = 2^n*A005809(n).
%F A228484 a(n) = A013609(3*n, n).
%F A228484 a(n) = A006588(n)/2^n.
%F A228484 a(n) = (2*n+1)*A153231(n).
%F A228484 Asymptotic approximation of a(n) ~ C*(13.5)^n/sqrt(n) with C = (1/2)*sqrt(3/Pi) = A137209.
%F A228484 Sum_{n>=0} 1/a(n) = (11*Pi - 12*log(2) + 270)/250. - _Amiram Eldar_, Mar 06 2022
%F A228484 From _Karol A. Penson_, Feb 26 2025: (Start)
%F A228484 G.f.: hypergeom([1/3,2/3],[1/2],27*z/2).
%F A228484 E.g.f.: hypergeom([1/3,2/3],[1/2,1],27*z/2). (End)
%p A228484 a := n -> 2^n*binomial(3*n, n): seq(a(n), n=0..16);
%t A228484 Table[2^n (3 n)!/(n! (2 n)!), {n, 0, 20}] (* _Vincenzo Librandi_, Aug 24 2013 *)
%o A228484 (Magma) [2^n*Factorial(3*n)/(Factorial(n)*Factorial(2*n)): n in [0..20]]; // _Vincenzo Librandi_, Aug 24 2013
%o A228484 (PARI) a(n) = 2^n*binomial(3*n, 2*n); \\ _Michel Marcus_, Mar 06 2022
%Y A228484 Cf. A005809, A013609, A006588, A137209.
%K A228484 nonn,easy
%O A228484 0,2
%A A228484 _Johannes W. Meijer_, Aug 22 2013
%E A228484 More terms from _Vincenzo Librandi_, Aug 24 2013