%I A141372
%S A141372 1,1,6,57,684,9512,146848,2455208,43764802,822963750,16203122280,
%T A141372 332189276516,7062047285812,155178233311932,3515420453148936,
%U A141372 81936668615592785,1961578144170589430,48167700575393576406
%N A141372 G.f. satisfies: A(x) = x + A(A(A(x)))^2.
%F A141372 G.f. satisfies: A( x - A(A(x))^2 ) = x.
%e A141372 G.f.: A(x) = x + x^2 + 6*x^3 + 57*x^4 + 684*x^5 + 9512*x^6 +...
%e A141372 A(A(x)) = x + 2*x^2 + 14*x^3 + 145*x^4 + 1848*x^5 + 26920*x^6 +...
%e A141372 A(A(A(x))) = x + 3*x^2 + 24*x^3 + 270*x^4 + 3658*x^5 + 55970*x^6 +...
%e A141372 A(A(A(x)))^2 = x^2 + 6*x^3 + 57*x^4 + 684*x^5 + 9512*x^6 +...
%e A141372 The series reversion of A(x) = x - A(A(x))^2, where
%e A141372 A(A(x))^2 = x^2 + 4*x^3 + 32*x^4 + 346*x^5 + 4472*x^6 + 65292*x^7 +...
%o A141372 (PARI) {a(n)=local(A=x+x^2);for(i=1,n,A=x+subst(A^2,x,subst(A,x,A+x*O(x^n))));
               polcoeff(A,n)}
%Y A141372 Cf. A141370, A141371.
%Y A141372 Sequence in context: A124556 A060435 A153851 this_sequence A152170 A087659 
               A107718
%Y A141372 Adjacent sequences: A141369 A141370 A141371 this_sequence A141373 A141374 
               A141375
%K A141372 nonn
%O A141372 1,3
%A A141372 Paul D. Hanna (pauldhanna(AT)juno.com), Jun 28 2008