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%I #5 Aug 15 2014 10:47:38
%S 0,1,2,4,10,28,92,328,1330,5740,27596,139160,769964,4423736,27567048,
%T 177127440,1223262698,8667225836,65523382052,506370134232,
%U 4150248267164,34679055629960,305773367599064,2742997917079984,25853946568986188
%N G.f. satisfies: A(x + x*A(-x)) = x + x*A(x).
%C Series reversion of g.f. A(x) is -A(-x). The g.f. for A006196 (leftist trees with n leaves) also satisfies this condition: A(-A(-x)) = x. This sequence was inspired by communication with Michael Somos, while he was investigating this and similar functional equations and their resulting sequences.
%H Vaclav Kotesovec, <a href="/A090594/b090594.txt">Table of n, a(n) for n = 0..270</a>
%F G.f.: A(-A(-x)) = x.
%o (PARI) {a(n)=local(A); if(n<0,0,A=x+x*O(x^n); for(i=1,n,B=subst(A,x,-x);C=subst(A,x,x+x*B);A=A+x+A*x-C); polcoeff(A,n,x))}
%Y Cf. A006196.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 05 2003
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