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%I #3 Jan 12 2019 19:49:52
%S 1,1,6,97,3708,286126,36084756,6508298392,1561731069408,
%T 477312184046536,180343755827049456,82394590229211894712,
%U 44740419997671632176608,28473068297755201366432096,20991426702927285864685894656,17750540113634768604238519234432,17068843562200262650028592424055808,18523905645979169633858014762594493056,22535986879713040510351902189004731737856,30550606589946151569429508183181183877223552
%N E.g.f. A(x) satisfies: A(x) = Sum_{n>=0} ( exp(2*n*x) - A(x)^n )^n.
%e E.g.f.: A(x) = 1 + x + 6*x^2/2! + 97*x^3/3! + 3708*x^4/4! + 286126*x^5/5! + 36084756*x^6/6! + 6508298392*x^7/7! + 1561731069408*x^8/8! + 477312184046536*x^9/9! + 180343755827049456*x^10/10! + ...
%e such that
%e A(x) = 1 + (exp(2*x) - A(x)) + (exp(4*x) - A(x)^2)^2 + (exp(6*x) - A(x)^3)^3 + (exp(8*x) - A(x)^4)^4 + (exp(10*x) - A(x)^5)^5 + (exp(12*x) - A(x)^6)^6 + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n,
%o A=concat(A,0); A=(A+Vec(sum(n=0,#A, (exp(2*x +x*O(x^#A))^n - Ser(A)^n)^n)))/2 ); n!*A[n+1]}
%o for(n=0,30,print1(a(n),", "))
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 12 2019