%I #15 Jun 03 2023 09:01:57

%S 1,3,9,54,270,1620,9828,61884,397062,2597508,17232831,115722918,

%T 784996434,5371325217,37029240315,256948639344,1793271890988,

%U 12579466538187,88645665923244,627235978623318,4454619888380355,31743030458459169,226890102674671245

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

%H Seiichi Manyama, <a href="/A363442/b363442.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+3*x^(k+1))^a(k).

%F 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 (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 Cf. A004111, A363441, A363443.

%Y Cf. A363426, A363439.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 02 2023