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 A103769 #16 May 13 2013 01:30:40
%S A103769 1,4,21,123,757,4788,30817,200784,1320093,8740284,58193673,389233287,
%T A103769 2613338091,17602627006,118892784555,804951501469,5461228061541,
%U A103769 37120212399708,252720891884473,1723088114793535,11763751150648785
%N A103769 Trinomial transform of central binomial coefficients A001405.
%H A103769 Vincenzo Librandi, <a href="/A103769/b103769.txt">Table of n, a(n) for n = 0..200</a>
%F A103769 a(n) = sum_{k=0..2n} T(n,k)*C(k,floor(k/2)), where T(n,k) is given by A027907.
%F A103769 a(n) = sum_{k=0..n} sum_{j=0..n} C(n,j)*C(j,k)*C(j+k,floor((j+k)/2)).
%F A103769 G.f.: ((3*x+1-(21*x^2-10*x+1)^(1/2))/(2*x*(3*x-4)*(7*x-1)))^(1/2). - _Mark van Hoeij_, Nov 16 2011
%F A103769 Conjecture: n*(2n+1)*a(n) +2(-61n^2+57n-20)*a(n-1) +3*(205n^2-523*n+346) * a(n-2) -72*(n-2)*(16n-33)*a(n-3) +567*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Dec 14 2011
%F A103769 a(n) ~ 7^(n+1/2)/sqrt(5*Pi*n). - _Vaclav Kotesovec_, Oct 24 2012
%t A103769 CoefficientList[Series[((3*x+1-(21*x^2-10*x+1)^(1/2))/(2*x*(3*x-4)*(7*x-1)))^(1/2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 24 2012 *)
%Y A103769 Cf. A082760.
%K A103769 easy,nonn
%O A103769 0,2
%A A103769 _Paul Barry_, Feb 15 2005