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A161971 E.g.f. satisfies: A(x) = exp( x*exp( x*A'(x) ) ), where A'(x) = d/dx A(x).

%I A161971 #5 Aug 24 2017 10:13:49
%S A161971 1,1,3,28,521,15596,672457,39049396,2919995969,272314100944,
%T A161971 30921124212881,4195725816103724,670156359448985521,
%U A161971 124435720115244671056,26578720273153614206201
%N A161971 E.g.f. satisfies: A(x) = exp( x*exp( x*A'(x) ) ), where A'(x) = d/dx A(x).
%H A161971 Vaclav Kotesovec, <a href="/A161971/b161971.txt">Table of n, a(n) for n = 0..230</a>
%F A161971 a(n) ~ c * n * (n!)^2, where c = 0.2773256592699... - _Vaclav Kotesovec_, Aug 24 2017
%e A161971 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 521*x^4/4! + 15596*x^5/5! +...
%e A161971 exp(x*A'(x)) = 1 + x + 7*x^2/2! + 103*x^3/3! + 2565*x^4/4! + 94881*x^5/5! +...
%e A161971 where log(A(x)) = x*exp(x*A'(x)):
%e A161971 log(A(x)) = x + 2*x^2/2! + 21*x^3/3! + 412*x^4/4! + 12825*x^5/5! + 569286*x^6/6! +...
%o A161971 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(x*exp(x*deriv(A)+O(x^n))));n!*polcoeff(A,n)}
%Y A161971 Cf. A161967 (variant).
%K A161971 nonn
%O A161971 0,3
%A A161971 _Paul D. Hanna_, Jun 23 2009