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A192131 G.f. satisfies: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^3*A(x)^k) * x^n/n ).

%I A192131 #8 Mar 30 2012 18:37:27
%S A192131 1,2,9,53,357,2611,20180,162276,1344455,11400944,98498545,864068233,
%T A192131 7677040177,68947431898,624960856374,5710352911097,52542826413590,
%U A192131 486458467209032,4528570067254485,42365044032385154,398081015128641213
%N A192131 G.f. satisfies: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^3*A(x)^k) * x^n/n ).
%e A192131 G.f.: A(x) = 1 + 2*x + 9*x^2 + 53*x^3 + 357*x^4 + 2611*x^5 + 20180*x^6 +...
%e A192131 where the g.f. satisfies:
%e A192131 log(A(x)) = (1 + A(x))*x + (1 + 8*A(x) + A(x)^2)*x^2/2 + (1 + 27*A(x) + 27*A(x)^2 + A(x)^3)*x^3/3 + (1 + 64*A(x) + 216*A(x)^2 + 64*A(x)^3 + A(x)^4)*x^4/4 +...
%o A192131 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^3*(A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}
%Y A192131 Cf. A007863 (variant).
%K A192131 nonn
%O A192131 0,2
%A A192131 _Paul D. Hanna_, Jun 24 2011