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A363471 G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} A(-x^k) * x^k/k ).

%I A363471 #16 Jun 04 2023 11:47:29
%S A363471 1,3,-3,-26,48,444,-920,-9126,19587,204214,-449496,-4841001,10856283,
%T A363471 119585034,-271813440,-3044796399,6991433415,79341313335,
%U A363471 -183641493481,-2105713558467,4905239040894,56722082044512,-132833292089826,-1546827734185557
%N A363471 G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} A(-x^k) * x^k/k ).
%H A363471 Seiichi Manyama, <a href="/A363471/b363471.txt">Table of n, a(n) for n = 0..1000</a>
%F A363471 A(x) = B(x)^3 where B(x) is the g.f. of A200402.
%F A363471 A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(3 * (-1)^k * a(k)).
%F A363471 a(0) = 1; a(n) = (3/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-1)^(d-1) * a(d-1) ) * a(n-k).
%o A363471 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(3*sum(k=1, i, subst(A, x, -x^k)*x^k/k)+x*O(x^n))); Vec(A);
%Y A363471 Cf. A006964, A200402, A363470.
%K A363471 sign
%O A363471 0,2
%A A363471 _Seiichi Manyama_, Jun 03 2023