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%I #6 Mar 30 2012 18:37:26
%S 1,2,9,64,574,5919,67205,820258,10602848,143710500,2028137178,
%T 29649220223,447247229447,6940546801219,110540089124381,
%U 1803424905623166,30092225956558590,512900050694933194
%N G.f. satisfies: x/(1-x) = A(x - A(x)^2).
%F G.f.: A(x) = G(x)/(1 - G(x)) where
%F * G(x) = A(x)/(1 + A(x)) and
%F * G(x) = Series_Reversion(x - A(x)^2).
%e G.f.: A(x) = x + 2*x^2 + 9*x^3 + 64*x^4 + 574*x^5 + 5919*x^6 +...
%e Related expansions.
%e x - A(x)^2 = x - x^2 - 4*x^3 - 22*x^4 - 164*x^5 - 1485*x^6 -...
%e Let G(x) equal the series reversion of x - A(x)^2, then
%e G(x) = x + x^2 + 6*x^3 + 47*x^4 + 442*x^5 + 4691*x^6 + 54330*x^7 +...
%e 1/(1-G(x)) = 1 + x + 2*x^2 + 9*x^3 + 64*x^4 + 574*x^5 + 5919*x^6 +...
%o (PARI) {a(n)=local(A=x+2*x^2,B=x/(1+x+x*O(x^n)));for(i=1,n,A=serreverse(B-subst(A,x,B)^2));polcoeff(A,n)}
%K nonn
%O 1,2
%A _Paul D. Hanna_, Feb 05 2011
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