%I #16 Jun 04 2023 11:47:29

%S 1,3,-3,-26,48,444,-920,-9126,19587,204214,-449496,-4841001,10856283,

%T 119585034,-271813440,-3044796399,6991433415,79341313335,

%U -183641493481,-2105713558467,4905239040894,56722082044512,-132833292089826,-1546827734185557

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

%H Seiichi Manyama, <a href="/A363471/b363471.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = B(x)^3 where B(x) is the g.f. of A200402.

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

%F 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 (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 Cf. A006964, A200402, A363470.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jun 03 2023