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A363442 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (3*x)^k/k ).

%I A363442 #15 Jun 03 2023 09:01:57
%S A363442 1,3,9,54,270,1620,9828,61884,397062,2597508,17232831,115722918,
%T A363442 784996434,5371325217,37029240315,256948639344,1793271890988,
%U A363442 12579466538187,88645665923244,627235978623318,4454619888380355,31743030458459169,226890102674671245
%N A363442 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k) * (3*x)^k/k ).
%H A363442 Seiichi Manyama, <a href="/A363442/b363442.txt">Table of n, a(n) for n = 0..1000</a>
%F A363442 A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+3*x^(k+1))^a(k).
%F A363442 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 A363442 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, x^k)*(3*x)^k/k)+x*O(x^n))); Vec(A);
%Y A363442 Cf. A004111, A363441, A363443.
%Y A363442 Cf. A363426, A363439.
%K A363442 nonn
%O A363442 0,2
%A A363442 _Seiichi Manyama_, Jun 02 2023