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G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * (3*x)^k/k ).
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%I #14 Jun 03 2023 09:01:51

%S 1,3,18,108,702,4698,32913,236844,1747170,13131639,100239444,

%T 774932832,6055105590,47742847875,379381851684,3035174325246,

%U 24426965179593,197622494260479,1606332527049645,13111628672610153,107428845309125157

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

%H Seiichi Manyama, <a href="/A363439/b363439.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = Sum_{k>=0} a(k) * x^k = 1/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, subst(A, x, x^k)*(3*x)^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A000081, A179469, A363440.

%Y Cf. A363423.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 02 2023