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G.f.: A(x) = x*exp( Sum_{n>=1} A(A(x)^n)/n ).
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%I #4 Mar 30 2012 18:37:22

%S 1,1,3,12,59,331,2062,13945,100981,775099,6260336,52914052,466062718,

%T 4263629043,40404127710,395772643255,4000017157615,41650278419675,

%U 446222379390064,4913287373304033,55545290608129184,644152152145611596

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

%F Euler transform equals A192637.

%F G.f. A(x) satisfies: Series_Reversion(A(x)) = x*Product_{n>=1} (1 - x^n)^a(n), where A(x) = Sum_{n>=1} a(n)*x^n.

%e G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 59*x^5 + 331*x^6 + 2062*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 +...

%e Log(A(x)/x) = x + 5*x^2/2 + 28*x^3/3 + 181*x^4/4 + 1271*x^5/5 + 9596*x^6/6 + 76665*x^7/7 + 642941*x^8/8 +...+ A179326(n)*x^n/n +...

%e The g.f. also satisfies:

%e x = A( x*(1-x)*(1-x^2)*(1-x^3)^3*(1-x^4)^12*(1-x^5)^59*(1-x^6)^331*... ).

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

%Y Cf. A179326, A192637.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jul 17 2010