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A363541 G.f. satisfies A(x) = exp( Sum_{k>=1} (3^k + A(x^k)) * x^k/k ).

%I A363541 #19 Jun 10 2023 10:56:16
%S A363541 1,4,17,73,324,1469,6838,32490,157398,775010,3870690,19567202,
%T A363541 99957231,515250057,2676884745,14002926871,73693381322,389904743248,
%U A363541 2072794614996,11066421965311,59310040841395,318978744562253,1720962766007827
%N A363541 G.f. satisfies A(x) = exp( Sum_{k>=1} (3^k + A(x^k)) * x^k/k ).
%H A363541 Seiichi Manyama, <a href="/A363541/b363541.txt">Table of n, a(n) for n = 0..1000</a>
%F A363541 A(x) = B(x)/(1 - 3*x) where B(x) is the g.f. of A363546.
%F A363541 A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-3*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).
%F A363541 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 3^k + Sum_{d|k} d * a(d-1) ) * a(n-k).
%o A363541 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (3^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
%Y A363541 Cf. A001678, A036249, A362389.
%Y A363541 Cf. A363507, A363543, A363546.
%K A363541 nonn
%O A363541 0,2
%A A363541 _Seiichi Manyama_, Jun 09 2023