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A363338 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^(3*k)) * x^k/k ).

%I A363338 #16 May 31 2023 10:48:39
%S A363338 1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,0,1,2,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0,1,
%T A363338 1,0,0,0,0,0,1,1,0,1,2,1,0,1,1,1,1,0,2,4,2,1,5,5,1,2,4,3,2,2,2,5,5,1,
%U A363338 4,8,4,1,5,5,2,2,2,3,4,2,1,5,5,2,3,4,2,1,3,3,2,2,5,6,3,5,8,5,2,5,6,6,6,4,9,15,9,6,17,16,5,9
%N A363338 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^(3*k)) * x^k/k ).
%H A363338 Seiichi Manyama, <a href="/A363338/b363338.txt">Table of n, a(n) for n = 0..1000</a>
%F A363338 A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+x^(3*k+1))^a(k).
%F A363338 A(x) * A(w*x) * A(w^2*x) = A(x^3), where w = exp(2*Pi*i/3).
%F A363338 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 3} (-1)^(k/d+1) * d * a(floor(d/3)) ) * a(n-k).
%o A363338 (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, x^(3*k))*x^k/k)+x*O(x^n))); Vec(A);
%Y A363338 Cf. A004111, A318133, A363339.
%Y A363338 Cf. A363336.
%K A363338 nonn
%O A363338 0,18
%A A363338 _Seiichi Manyama_, May 28 2023