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%I #22 Mar 26 2023 10:47:55
%S 1,2,30,672,18150,546546,17672928,600935040,21212454582,770748371250,
%T 28657235757150,1085694550387200,41778588391394400,
%U 1628982594897249312,64234570537702934400,2557710564063135005184,102714012593435476016982,4155894894567674772785250,169274181059121504574121550,6935873114065443534326340000,285716428631735196825345889350,11826871503027977442890882704050,491714173272153004121882711232000
%N a(n) = binomial(3*n-1,n) * binomial(3*n,n)/(2*n+1).
%C Central terms of triangles A278881 and A278882; a(n) = A278881(2*n,n) for n>=0.
%H Seiichi Manyama, <a href="/A278884/b278884.txt">Table of n, a(n) for n = 0..606</a>
%F 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
%t Table[(Binomial[3n-1,n]Binomial[3n,n])/(2n+1),{n,0,50}] (* _Harvey P. Dale_, Mar 26 2023 *)
%o (PARI) {a(n) = binomial(3*n-1,n) * binomial(3*n,n) / (2*n+1)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A278881, A278882.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 29 2016
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