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%I #12 Mar 16 2013 17:10:03
%S 1,1,3,16,149,1956,33487,710914,18051945,534541240,18111042971,
%T 691843182174,29448194808397,1383323874167860,71145082349453127,
%U 3979392388532436586,240697239447634403153,15667133474066968379376,1092794908568878699158835,81380508121010249600574646
%N E.g.f. satisfies: A(x) = Sum_{n>=0} x^n * exp(n*x*A(x)^n) / n!.
%C Compare to: W(x) = Sum_{n>=0} x^n * exp(n*x*W(x)) / n! where W(x) = Sum_{n>=0} (n+1)^(n-1)*x^n/n!.
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 149*x^4/4! + 1956*x^5/5! +...
%e where
%e A(x) = 1 + x*exp(x*A(x)) + x^2*exp(2*x*A(x)^2)/2! + x^3*exp(3*x*A(x)^3)/3! + x^4*exp(4*x*A(x)^4)/4! +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/m!*exp(m*x*A^m+x*O(x^n)))); n!*polcoeff(A, n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A217251, A000272.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Mar 09 2013
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