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 A141344 #10 Jan 30 2020 21:58:01
%S A141344 1,1,3,7,19,45,123,285,807,1771,5407,10587,37627,57619,279783,231615,
%T A141344 2307339,-387531,21769251,-28249347,235837791,-539858235,2857845723,
%U A141344 -8509970007,37342507167,-126289733319,510715973643,-1837291760147
%N A141344 Expansion of (2-sqrt(1+4x))/(2-x-sqrt(1+4x)).
%C A141344 Row sums of A141343. Hankel transform is 2^n.
%C A141344 Image of A052961 under the Riordan array (c(-x),xc(-x)^2), c(x) the g.f. of A000108. [From _Paul Barry_, Jan 29 2009]
%F A141344 Conjectured to be D-finite with recurrence: 3*(n-1)*a(n) +2*(2*n-11)*a(n-1) +(79-31*n)*a(n-2) +2*(2*n-5)*a(n-3)=0. - _R. J. Mathar_, Oct 25 2012
%t A141344 CoefficientList[Series[(2-Sqrt[1+4x])/(2-x-Sqrt[1+4x]),{x,0,30}],x] (* _Harvey P. Dale_, Jan 14 2013 *)
%K A141344 easy,sign
%O A141344 0,3
%A A141344 _Paul Barry_, Jun 26 2008