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G.f.: A(x) = G(G(x)) where G(x) = x*exp( Sum_{n>=1} A(x^n)/n ).
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%I #2 Mar 30 2012 18:37:22

%S 1,2,8,38,212,1309,8818,63599,486431,3914297,32957543,289117257,

%T 2633818459,24851646254,242360970744,2438642027680,25279637797827,

%U 269638473505847,2955984372213381,33274178272368580,384251966241266988

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

%e G.f.: A(x) = x + 2*x^2 + 8*x^3 + 38*x^4 + 212*x^5 + 1309*x^6 +...

%e G(x) = x + x^2 + 3*x^3 + 11*x^4 + 52*x^5 + 280*x^6 + 1705*x^7 + 11275*x^8 + 80120*x^9 + 604111*x^10 +...+ A179322(n)*x^n +...

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

%e log(G(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 +...

%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(subst(A,x,A),n)}

%Y Cf. A179322, A179324.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jul 16 2010