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A140046 G.f. satisfies: A(x) = x/(1 - A(x+x^2)).

%I A140046 #2 Mar 30 2012 18:37:10
%S A140046 1,1,3,10,41,186,922,4911,27830,166656,1049410,6922476,47698148,
%T A140046 342483885,2557538781,19829608532,159393394129,1326509171669,
%U A140046 11415703608635,101473987987073,930688926616454,8798656042121634
%N A140046 G.f. satisfies: A(x) = x/(1 - A(x+x^2)).
%e A140046 G.f.: A(x) = x + x^2 + 3*x^3 + 10*x^4 + 41*x^5 + 186*x^6 + 922*x^7 +...
%e A140046 A(x+x^2) = x + 2*x^2 + 5*x^3 + 20*x^4 + 90*x^5 + 454*x^6 + 2488*x^7 +...
%e A140046 Let B(x) = x + x^2; define B_{n+1}(x) = B( B_{n}(x) ) with B_0(x)=x;
%e A140046 then g.f. A(x) equals the continued fraction:
%e A140046 A(x) = x/(1 - B(x)/(1 - B_2(x)/(1 - B_3(x)/(1 - B_4(x)/(1 - ...)))))
%e A140046 where B_{n}(x) begin:
%e A140046 B_2(x) = x + 2*x^2 + 2*x^3 + x^4 ;
%e A140046 B_3(x) = x + 3*x^2 + 6*x^3 + 9*x^4 + 10*x^5 + 8*x^6 + 4*x^7 + x^8 ;
%e A140046 B_4(x) = x + 4*x^2 + 12*x^3 + 30*x^4 + 64*x^5 + 118*x^6 + 188*x^7 +...;
%e A140046 B_5(x) = x + 5*x^2 + 20*x^3 + 70*x^4 + 220*x^5 + 630*x^6 + 1656*x^7 +...
%o A140046 (PARI) {a(n)=local(A=x);if(n==0,A=x,for(i=1,n,A=x/(1-subst(A,x,x+x^2 +x*O(x^n))))); polcoeff(A,n)}
%Y A140046 Cf. A127782.
%K A140046 nonn
%O A140046 1,3
%A A140046 _Paul D. Hanna_, May 09 2008