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 A166697 #15 May 24 2016 10:24:58
%S A166697 1,4,25,187,1552,13771,127927,1228576,12099751,121538581,1240336660,
%T A166697 12824049277,134043231781,1414108869268,15037450664317,
%U A166697 161014687970191,1734550886346592,18785969304551263,204432608804093155
%N A166697 A "Morgan Voyce" transform of A103210.
%C A166697 Partial sums of A166696.
%H A166697 G. C. Greubel, <a href="/A166697/b166697.txt">Table of n, a(n) for n = 0..500</a>
%F A166697 G.f.: (1-3x+x^2-sqrt(1-14x+27x^2-14x^3+x^4))/(4x(1-x));
%F A166697 G.f.: 1/(1-x-3x/(1-x-2x/(1-x-3x/(1-x-2x/(1-x-3x/(1-x-2x/(1-.... (continued fraction);
%F A166697 a(n) = Sum_{k=0..n} C(n+k,2k)*A103210(k).
%F A166697 a(n) = Sum_{k=0..n} A085478(n,k)*A103210(k). - _Philippe Deléham_, Nov 16 2013
%F A166697 Conjecture: (n+1)*a(n) + 3*(-5*n+2)*a(n-1) + (41*n-61)*a(n-2) + (-41*n+103)*a(n-3) + 3*(5*n-18)*a(n-4) + (-n+5)*a(n-5) = 0. - _R. J. Mathar_, Feb 10 2015
%p A166697 A166697 := proc(n)
%p A166697 add(A166696(k),k=0..n) ;
%p A166697 end proc: # _R. J. Mathar_, Feb 10 2015
%t A166697 CoefficientList[Series[(1 - 3*t + t^2 - Sqrt[1 - 14*t + 27*t^2 - 14*t^3 + t^4])/(4*t*(1 - t)), {t, 0, 50}], t] (* _G. C. Greubel_, May 23 2016 *)
%Y A166697 Cf. A085478, A103210, A166696
%K A166697 easy,nonn
%O A166697 0,2
%A A166697 _Paul Barry_, Oct 18 2009