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 A278884 #27 Sep 04 2025 09:20:26
%S A278884 1,2,30,672,18150,546546,17672928,600935040,21212454582,770748371250,
%T A278884 28657235757150,1085694550387200,41778588391394400,
%U A278884 1628982594897249312,64234570537702934400,2557710564063135005184,102714012593435476016982,4155894894567674772785250,169274181059121504574121550,6935873114065443534326340000,285716428631735196825345889350,11826871503027977442890882704050,491714173272153004121882711232000
%N A278884 a(n) = binomial(3*n-1,n) * binomial(3*n,n)/(2*n+1).
%C A278884 Central terms of triangles A278881 and A278882; a(n) = A278881(2*n,n) for n>=0.
%H A278884 Seiichi Manyama, <a href="/A278884/b278884.txt">Table of n, a(n) for n = 0..606</a>
%F A278884 4*n^2*(2*n-1)*(2*n+1)*a(n) - 9*(3*n-1)^2*(3*n-2)^2*a(n-1) = 0. - _R. J. Mathar_, Dec 02 2016
%F A278884 From _Stefano Spezia_, Sep 04 2025: (Start)
%F A278884 G.f.: (1 + 2*hypergeom([1/3, 1/3, 2/3, 2/3], [1/2, 1, 3/2],9^3*x/2^4])/3.
%F A278884 a(n) ~ 4^(-2*n-1)*9^(3*n)/(n^2*Pi). (End)
%t A278884 Table[(Binomial[3n-1,n]Binomial[3n,n])/(2n+1),{n,0,50}] (* _Harvey P. Dale_, Mar 26 2023 *)
%o A278884 (PARI) {a(n) = binomial(3*n-1,n) * binomial(3*n,n) / (2*n+1)}
%o A278884 for(n=0,20,print1(a(n),", "))
%Y A278884 Cf. A278881, A278882.
%K A278884 nonn,changed
%O A278884 0,2
%A A278884 _Paul D. Hanna_, Nov 29 2016