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 A228002 #22 Nov 02 2016 13:44:16
%S A228002 1,3,33,367,4533,58971,794805,10983819,154653081,2209251319,
%T A228002 31925528217,465708778407,6846750893929,101325729466071,
%U A228002 1508015866093929,22553429144856471,338744206097695629,5106973783924992771,77251106929381097229,1172036566162209342771
%N A228002 Alternate partial sums of binomial(2n,n)^2.
%H A228002 Seiichi Manyama, <a href="/A228002/b228002.txt">Table of n, a(n) for n = 0..833</a>
%F A228002 Recurrence: n^2*a(n) = (3*n-2)*(5*n-2)*a(n-1) + 4*(2*n-1)^2*a(n-2).
%F A228002 a(n) ~ 16^(n+1)/(17*Pi*n).
%p A228002 series(2*EllipticK(4*x^(1/2))/(Pi*(1+x)),x=0,20)
%t A228002 Table[Sum[(-1)^(n-k)*Binomial[2*k,k]^2, {k, 0, n}], {n, 0, 20}]
%Y A228002 Cf. A115257, A188679, A188680.
%K A228002 nonn,easy
%O A228002 0,2
%A A228002 _Vaclav Kotesovec_, Aug 07 2013