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

%S 1,3,7,23,51,201,442,1663,4156,15083,35564,139961,329694,1244834,

%T 3162552,11494207,28340038,108476634,266695553,992977283,2544862201,

%U 9319498334,23550935216,87424092169,222620040051,819109845024

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

%e L.g.f.: Log(G(x)) = x + 3*x^2/2 + 7*x^3/3 + 23*x^4/4 + 51*x^5/5 + 201*x^6/6 + 442*x^7/7 + 1663*x^8/8 + 4156*x^9/9 +...+ a(n)*x^n/n +...

%e G(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 22*x^5 + 63*x^6 + 148*x^7 + 429*x^8 + 1093*x^9 + 3233*x^10 + 8235*x^11 +...+ A179490(n)*x^n +...

%e Log(G(x)) = G(x)*x + G(3*x^2)*x^2/2 + G(7*x^3)*x^3/3 + G(23*x^4)*x^4/4 + G(51*x^5)*x^5/5 + G(201*x^6)*x^6/6 +...+ G(a(n)*x^n)*x^n/n +...

%o (PARI) {a(n)=local(A=[1,1],L=[1]);for(i=1,n+1, A=Vec(exp(sum(n=1,#A-1,subst(Ser(A),x,L[n]*x^n)*x^n/n)+O(x^#A))); A=concat(A,0);L=Vec(deriv(log(Ser(A)))));L[n+1]}

%Y Cf. A179490.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 16 2010