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%I #5 Jun 07 2012 17:05:24
%S 1,1,1,2,5,12,30,80,219,609,1724,4953,14388,42193,124768,371602,
%T 1113667,3356017,10162979,30911457,94390590,289258448,889304859,
%U 2742205395,8478653638,26280715255,81648362339,254204771596,793011895972,2478427376313,7759251412310
%N G.f. satisfies: A(x) = x + A( A(x)^2/(1 + A(x)) ).
%C Compare g.f. to: G(x) = x + G( G(x)^2/(1 + G(x) + G(x)^2) ) when G(x) = x/(1-x).
%e G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 12*x^6 + 30*x^7 + 80*x^8 +...
%e Related expansions:
%e A(x)^2 = x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 15*x^6 + 38*x^7 + 98*x^8 +...
%e A(x)^2/(1 + A(x)) = x^2 + x^3 + x^4 + 3*x^5 + 8*x^6 + 19*x^7 + 49*x^8 +...
%o (PARI) {a(n)=local(A=x+x^2);for(i=1,n,A=x+subst(A,x,A^2/(1+A+x*O(x^n))));polcoeff(A,n)}
%o for(n=1,40,print1(a(n),", "))
%Y Cf. A213264.
%K nonn
%O 1,4
%A _Paul D. Hanna_, Jun 07 2012
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