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%I #2 Mar 30 2012 18:37:15
%S 1,2,7,30,155,950,6706,52996,459256,4303020,43163392,460170882,
%T 5184956805,61468942912,763967696243,9924157671028,134400823231643,
%U 1893397004671954,27693154054839058,419804185629085664
%N G.f. A(x) satisfies: A(x) = x + 2*x*A(x) + 3*x^2*A(A(x)) + 4*x^3*A(A(A(x))) +...
%e G.f.: A(x) = x + 2*x*A(x) + 3*x^2*A(A(x)) + 4*x^3*A(A(A(x))) +...
%e where the initial iterations of the g.f. A(x) begin:
%e A(x) = x + 2*x^2 + 7*x^3 + 30*x^4 + 155*x^5 + 950*x^6 + 6706*x^7 +...;
%e A(A(x)) = x + 4*x^2 + 22*x^3 + 138*x^4 + 957*x^5 + 7242*x^6 +...;
%e A(A(A(x))) = x + 6*x^2 + 45*x^3 + 372*x^4 + 3294*x^5 + 30858*x^6 +...;
%e A(A(A(A(x)))) = x + 8*x^2 + 76*x^3 + 780*x^4 + 8438*x^5 + 95156*x^6 +...;
%e A(A(A(A(A(x))))) = x + 10*x^2 + 115*x^3 + 1410*x^4 + 18045*x^5 +...; ...
%e so: a(1)=1, a(2)=2, a(3) = 2*2 + 3 = 7, a(4) = 2*7 + 3*4 + 4 = 30, ...
%o (PARI) {a(n)=local(F=x+x*O(x^n), G=F, H=x); for(i=1, n, for(k=1, n, G=subst(F, x, G); H=H+(k+1)*x^k*G); F=H; G=x+x*O(x^n); H=G); polcoeff(F, n)}
%Y Cf. A120567.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Jan 05 2009
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