A141149 - OEIS

%I #2 Mar 30 2012 18:37:10

%S 1,2,10,74,682,7274,86386,1116338,15464818,227315378,3519165370,

%T 57067589306,965272138714,16974057490010,309490272908386,

%U 5838392491816418,113747315349651298,2285212240930687202

%N G.f. satisfies: A(x) = x*(1 + A(A(x)))/(1 - A(A(x))).

%F G.f. satisfies: A( x*(1 - A(x))/(1 + A(x)) ) = x.

%e A(x) = x + 2*x^2 + 10*x^3 + 74*x^4 + 682*x^5 + 7274*x^6 + 86386*x^7 +...

%e A(A(x)) = x + 4*x^2 + 28*x^3 + 256*x^4 + 2752*x^5 + 33124*x^6 + 434524*x^7 +...

%e The series reversion of A(x) equals:

%e x*(1-A(x))/(1+A(x)) = x - 2*x^2 - 2*x^3 - 14*x^4 - 110*x^5 - 1058*x^6 -...

%o (PARI) {a(n)=local(A=x+x^2); if(n<1, 0, for(i=1,n,A=serreverse(x*((1-A)/(1+A+x*O(x^n))))); polcoeff(A, n))}

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 11 2008