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 A103821 #11 May 13 2013 01:30:47
%S A103821 1,3,11,43,179,771,3395,15171,68515,311907,1428835,6578531,30414435,
%T A103821 141105251,656588899,3063038051,14321092195,67088405091,314825048675,
%U A103821 1479654425187,6963888239203,32815960756835,154813864252003
%N A103821 A Whitney transform of the central binomial coefficients A000984.
%C A103821 Partial sums of A006139. The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)).
%H A103821 Vincenzo Librandi, <a href="/A103821/b103821.txt">Table of n, a(n) for n = 0..200</a>
%F A103821 G.f. : 1/((1-x)sqrt(1-4x-4x^2));
%F A103821 a(n)=sum{k=0..n, sum{i=0..n, C(k, i-k)}*C(2k, k)}.
%F A103821 Conjecture: n*a(n) +(2-5n)*a(n-1) +2*a(n-2)+4*(n-1)*a(n-3)=0. - R. J. Mathar, Dec 14 2011
%F A103821 a(n) ~ sqrt(34+23*sqrt(2))*(2+2*sqrt(2))^n/(7*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 17 2012
%t A103821 CoefficientList[Series[1/((1-x)*Sqrt[1-4*x-4*x^2]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 17 2012 *)
%K A103821 easy,nonn
%O A103821 0,2
%A A103821 _Paul Barry_, Feb 16 2005