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A363439 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ).

%I A363439 #14 Jun 03 2023 09:01:51
%S A363439 1,3,18,108,702,4698,32913,236844,1747170,13131639,100239444,
%T A363439 774932832,6055105590,47742847875,379381851684,3035174325246,
%U A363439 24426965179593,197622494260479,1606332527049645,13111628672610153,107428845309125157
%N A363439 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ).
%H A363439 Seiichi Manyama, <a href="/A363439/b363439.txt">Table of n, a(n) for n = 0..1000</a>
%F A363439 A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-3*x^(k+1))^a(k).
%F A363439 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} d * 3^(k/d) * a(d-1) ) * a(n-k).
%o A363439 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*(3*x)^k/k)+x*O(x^n))); Vec(A);
%Y A363439 Cf. A000081, A179469, A363440.
%Y A363439 Cf. A363423.
%K A363439 nonn
%O A363439 0,2
%A A363439 _Seiichi Manyama_, Jun 02 2023