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%I #17 May 31 2023 10:48:44
%S 1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,2,1,0,0,1,1,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,2,1,0,0,1,1,0,0,0,0,0,1,1,0,0,2,4,2,0,1,5,5,1,0
%N G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^(4*k)) * x^k/k ).
%H Seiichi Manyama, <a href="/A363339/b363339.txt">Table of n, a(n) for n = 0..1000</a>
%F A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+x^(4*k+1))^a(k).
%F A(x) * A(i*x) * A(-x) * A(i^3*x) = A(-x^4), where i=sqrt(-1).
%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 4} (-1)^(k/d+1) * d * a(floor(d/4)) ) * a(n-k).
%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, (-1)^(k+1)*subst(A, x, x^(4*k))*x^k/k)+x*O(x^n))); Vec(A);
%Y Cf. A004111, A318133, A363338.
%Y Cf. A363337.
%K nonn
%O 0,27
%A _Seiichi Manyama_, May 28 2023
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