%I A135052
%S A135052 1,1,3,7,19,51,143,407,1183,3487,10415,31439,95791,294191,909823,
%T A135052 2830943,8856255,27839167,87888767,278545663,885903743,2826612095,
%U A135052 9045147391,29022168063,93350430975,300949170431,972271227647
%N A135052 Expansion of (1-2x-sqrt(1-4x+8x^3-4x^4))/(2x^2(1-x)).
%C A135052 Sequence is the binomial transform of the aerated large Schroeder numbers 
               A006318. Hankel transform is A060656(n+1).
%F A135052 a(n)=sum{k=0..n, sum{j=0..k/2, C(k/2+j, 2j)*C(j)*(1+(-1)^k)/2}}, where 
               C(n)=A000108(n).
%F A135052 G.f.: 1/(1-x-2x^2/(1-x-x^2/(1-x-2x^2/(1-x-x^2/(1-x-2x^2.... (continued 
               fraction); [From Paul Barry (pbarry(AT)wit.ie), Jan 02 2009]
%Y A135052 Sequence in context: A002426 A011769 A087432 this_sequence A146597 A115254 
               A090378
%Y A135052 Adjacent sequences: A135049 A135050 A135051 this_sequence A135053 A135054 
               A135055
%K A135052 easy,nonn
%O A135052 0,3
%A A135052 Paul Barry (pbarry(AT)wit.ie), Nov 15 2007