%I A134824
%S A134824 0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A134824 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A134824 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%V A134824 0,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
               -1,-1,-1,-1,-1,
%W A134824 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
               -1,-1,-1,-1,-1,
%X A134824 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
               -1,-1,-1,-1,-1
%N A134824 Generated by reverse of Schroeder II o.g.f.
%C A134824 The o.g.f. S(x) for A001003 (Schroeder II) satisfies 2*S^2(x) + (1+x)*S(x) 
               + x = 0.
%C A134824 Using the Lagrange series for y=S(x) with y=0+x*(y/A(y)) leads to the 
               formula for Schroeder II numbers involving the Narayana triangle 
               A001263. See the Narayana comment by B. Cloitre under A001003 and 
               a multiple differentiation formula given there.
%F A134824 G.f. A(x)= x*(1-2*x)/(1-x).
%F A134824 a(0)=0,a(1)=1, a(n)=-1, n>=2.
%Y A134824 Sequence in context: A057428 A062157 A112347 this_sequence A000007 A014041 
               A015868
%Y A134824 Adjacent sequences: A134821 A134822 A134823 this_sequence A134825 A134826 
               A134827
%K A134824 sign,easy
%O A134824 0,1
%A A134824 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 13 2007