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 A188683 #23 Nov 03 2016 09:30:57
%S A188683 1,2,43,965,26260,793559,25715833,875686727,30942995146,1125179561729,
%T A188683 41860674073996,1586681151506804,61081201435584796,
%U A188683 2382392690910289172,93969463115644112428,3742596382979058395348
%N A188683 Alternate partial sums of binomial(3n,n)^2/(2n+1).
%H A188683 Seiichi Manyama, <a href="/A188683/b188683.txt">Table of n, a(n) for n = 0..606</a>
%F A188683 a(n) = sum(binomial(3*k,k)^2*(-1)^(n-k)/(2*k+1), k=0..n).
%F A188683 Recurrence: 4*(n+2)^2*(4*n^2+16*n+15) * a(n+2) -(713*n^4+4246*n^3 +9421*n^2 +9224*n+3360) * a(n+1) -9*(9*n^2+27*n+20)^2 * a(n) = 0.
%F A188683 a(n) ~ 3^(6*n+7)/(745*Pi*n^2*2^(4*n+3)). - _Vaclav Kotesovec_, Aug 06 2013
%t A188683 Table[Sum[Binomial[3k,k]^2(-1)^(n-k)/(2k+1),{k,0,n}],{n,0,20}]
%o A188683 (Maxima) makelist(sum(binomial(3*k,k)^2*(-1)^(n-k)/(2*k+1),k,0,n),n,0,20);
%Y A188683 Cf. A005809, A001764, A188676, A104859, A188678, A188681, A188686, A188687.
%Y A188683 Cf. Alternate partial sums of binomial(3n,n)^2/(2n+1)^k: A188680 (k=0), this sequence (k=1), A188685 (k=2).
%Y A188683 Cf. Partial sums of binomial(3n,n)^2/(2n+1)^k: A188679 (k=0), A188682 (k=1), A188684 (k=2).
%K A188683 nonn,easy
%O A188683 0,2
%A A188683 _Emanuele Munarini_, Apr 08 2011