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A384689 E.g.f. A(x) satisfies A(x) = exp( x*A(x)^2 * A(x*A(x)) ).

%I A384689 #11 Jun 07 2025 08:21:44
%S A384689 1,1,7,106,2593,89796,4085029,232694806,16053415249,1308960150472,
%T A384689 123811136509861,13387049625793746,1635128238889494793,
%U A384689 223420020463904387020,33872693045213102767093,5658826351169923606739206,1035543935182601250745181089,206506472947550295487980305424
%N A384689 E.g.f. A(x) satisfies A(x) = exp( x*A(x)^2 * A(x*A(x)) ).
%F A384689 See A384690.
%t A384689 terms = 18; A[_] = 0; Do[A[x_] = Exp[x*A[x]^2*A[x*A[x]]] + O[x]^terms // Normal, terms]; Range[0,terms-1]!CoefficientList[A[x], x] (* _Stefano Spezia_, Jun 07 2025 *)
%o A384689 (PARI) a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, (n+j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
%Y A384689 Column k=1 of A384690.
%Y A384689 Cf. A140049.
%K A384689 nonn
%O A384689 0,3
%A A384689 _Seiichi Manyama_, Jun 07 2025