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%I #10 Jun 10 2023 09:57:30
%S 1,-1,2,-2,4,-6,13,-20,38,-65,129,-228,435,-794,1528,-2833,5421,
%T -10189,19561,-37091,71247,-135973,261879,-502303,969181,-1866210,
%U 3608664,-6970576,13504298,-26152744,50758711,-98515611,191517618,-372404560,725061378
%N G.f. satisfies A(x) = exp( Sum_{k>=1} ((-2)^k + A(x^k)) * x^k/k ).
%F A(x) = B(x)/(1 + 2*x) where B(x) is the g.f. of A363580.
%F A(x) = Sum_{k>=0} a(k) * x^k = 1/(1+2*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).
%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( (-2)^k + Sum_{d|k} d * a(d-1) ) * a(n-k).
%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, ((-2)^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);
%Y Cf. A001678, A036249, A362389, A363541, A363579.
%Y Cf. A363580.
%K sign
%O 0,3
%A _Seiichi Manyama_, Jun 10 2023
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