cp's OEIS Frontend

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.

A026019 a(n) = binomial(3*n,n) - binomial(3*n,n-3).

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%I A026019 #20 May 10 2020 17:27:24
%S A026019 1,3,15,83,483,2898,17748,110295,692967,4390815,28009215,179652564,
%T A026019 1157534420,7486680048,48579667704,316107403839,2061920664351,
%U A026019 13478362911825,88272020923485,579081767982795,3804622827123195
%N A026019 a(n) = binomial(3*n,n) - binomial(3*n,n-3).
%F A026019 G.f.: (1-2*g)*(g^2-g+1)/((3*g-1)*(g-1)^3) where g*(1-g)^2 = x. - _Mark van Hoeij_, Nov 09 2011
%F A026019 Conjecture: -2*(2*n+3)*(13*n-9)*(n+1)*a(n) +(499*n^3-7*n^2-120*n-54)*a(n-1) -3*(3*n-5)*(37*n-24)*(3*n-4)*a(n-2)=0. - _R. J. Mathar_, Jun 20 2013
%t A026019 Table[Binomial[3n,n]-Binomial[3n,n-3],{n,0,20}] (* _Harvey P. Dale_, Jun 04 2016 *)
%o A026019 (PARI) a(n) = binomial(3*n,n) - binomial(3*n,n-3); \\ _Michel Marcus_, May 10 2020
%Y A026019 a(n) = T(3n, n), where T is the array defined in A026009.
%K A026019 nonn,easy
%O A026019 0,2
%A A026019 _Clark Kimberling_
%E A026019 More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 17 2005