%I A161605
%S A161605 1,1,3,28,365,6496,147127,4033408,130058777,4822981120,202225551371,
%T A161605 9460961327104,488602134968389,27609977350868992,1694576741234926655,
%U A161605 112258296102497099776,7983577042683934226993,606688287932557859356672
%N A161605 E.g.f. satisfies: A(x) = exp(x*exp(x*A(x)^3)).
%C A161605 More generally, if G(x) = exp(x*exp(x*G(x)^p)),
%C A161605 where G(x)^m = Sum_{n>=0} g(n,m)*x^n/n!,
%C A161605 then g(n,m) = Sum_{k=0..n} C(n,k) * m*(p*(n-k) + m)^(k-1) * k^(n-k).
%F A161605 a(n) = Sum_{k=0..n} C(n,k) * (3*(n-k) + 1)^(k-1) * k^(n-k).
%e A161605 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 365*x^4/4! +...
%o A161605 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*(3*(n-k)+1)^(k-1)*k^(n-k))}
%o A161605 (PARI) {a(n)=local(A=1+x);for(i=0,n,A=exp(x*exp(x*A^3+O(x^n))));n!*polcoeff(A,
               n,x)}
%Y A161605 Cf. A161552, A161567.
%Y A161605 Sequence in context: A026114 A072343 A151423 this_sequence A048954 A086569 
               A143636
%Y A161605 Adjacent sequences: A161602 A161603 A161604 this_sequence A161606 A161607 
               A161608
%K A161605 nonn
%O A161605 0,3
%A A161605 Paul D. Hanna (pauldhanna(AT)juno.com), Jun 14 2009