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A161967 E.g.f. satisfies: A(x) = exp( x*exp( x*A'(x)/A(x) ) ), where A'(x)/A(x) = d/dx log(A(x)).

%I A161967 #2 Mar 30 2012 18:37:17
%S A161967 1,1,3,22,317,7596,270727,13332544,862740153,70762448080,
%T A161967 7161344443691,875732817920544,127244974218410677,
%U A161967 21666397760623131712,4273075677258426773295,966395699152796722817536
%N A161967 E.g.f. satisfies: A(x) = exp( x*exp( x*A'(x)/A(x) ) ), where A'(x)/A(x) = d/dx log(A(x)).
%e A161967 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 317*x^4/4! + 7596*x^5/5! +...
%e A161967 A'(x)/A(x) = 1 + 2*x + 15*x^2/2! + 232*x^3/3! + 5905*x^4/4! + 220176*x^5/5! +...
%e A161967 where x*exp( x*d/dx log(A(x)) ) = log(A(x)) = e.g.f. of A161968.
%o A161967 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(x*exp(x*deriv(A)/(A+O(x^n)))));n!*polcoeff(A,n)}
%Y A161967 Cf. A161968 (log).
%K A161967 nonn
%O A161967 0,3
%A A161967 _Paul D. Hanna_, Jun 23 2009