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A179322 G.f.: A(x) = x*exp( Sum_{n>=1} A(A(x^n))/n ). 2

%I #2 Mar 30 2012 18:37:22

%S 1,1,3,11,52,280,1705,11275,80120,604111,4798905,39929804,346524607,

%T 3125963037,29233335516,282788639070,2824492759211,29083164399395,

%U 308309674727517,3361022281811994,37639685125200313,432621284744483040

%N G.f.: A(x) = x*exp( Sum_{n>=1} A(A(x^n))/n ).

%e G.f.: A(x) = x + x^2 + 3*x^3 + 11*x^4 + 52*x^5 + 280*x^6 + 1705*x^7 +...

%e log(A(x)/x) = A(A(x)) + A(A(x^2))/2 + A(A(x^3))/3 + A(A(x^4))/4 + A(A(x^5))/5 + A(A(x^6))/6 +...+ A(A(x^n))/n +...

%e log(A(x)/x) = x + 5*x^2/2 + 25*x^3/3 + 157*x^4/4 + 1061*x^5/5 + 7883*x^6/6 + 61727*x^7/7 + 508949*x^8/8 +...+ A179324(n)*x^n/n +...

%e A(A(x)) = x + 2*x^2 + 8*x^3 + 38*x^4 + 212*x^5 + 1309*x^6 + 8818*x^7 + 63599*x^8 + 486431*x^9 + 3914297*x^10 +...+ A179323(n)*x^n +...

%o (PARI) {a(n)=local(A=x);for(i=1,n,A=x*exp(sum(m=1,n,subst(A,x,(subst(A,x,x^m+x*O(x^n))))/m)));polcoeff(A,n)}

%Y Cf. A179323, A179324.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jul 16 2010

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