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%I #13 Mar 12 2022 13:13:02
%S 1,1,1,2,5,12,30,80,221,624,1798,5271,15662,47052,142686,436187,
%T 1342669,4158048,12945758,40497415,127225426,401222453,1269712425,
%U 4030877287,12833659158,40968993548,131106215470,420507819784,1351562339222,4352564765053,14042486582525
%N G.f. satisfies: A(x) = 1 + x*A(x) * A( x^2*A(x)^2 ).
%F G.f. satisfies: A( x/(1 + x*A(x^2)) ) = 1 + x*A(x^2).
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 12*x^5 + 30*x^6 + 80*x^7 +...
%e Related expansions.
%e 1/(1+x*A(x^2)) = 1 - x + x^2 - 2*x^3 + 3*x^4 - 5*x^5 + 8*x^6 - 14*x^7 +...
%e compare to the series reversion of x*A(x), which begins:
%e x - x^2 + x^3 - 2*x^4 + 3*x^5 - 5*x^6 + 8*x^7 - 14*x^8 + 23*x^9 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1/x*serreverse(x/(1+x*subst(A,x,x^2 +x*O(x^n)))));polcoeff(A,n)}
%o for(n=0,31,print1(a(n),", "))
%K nonn
%O 0,4
%A _Paul D. Hanna_, May 02 2012
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