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%I #8 Jun 20 2022 08:36:23
%S 1,1,3,25,611,41721,7326115,3120454233,3105527125475,7041597540281017,
%T 35733375744777784867,400526056950063657595929,
%U 9816824637930442994222501475,521959475771315485798501882623609,59814953381855591853355367174623538851
%N E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(2 * (1 - exp(-x))).
%F E.g.f. A(x) satisfies: A(-log(1-x)) = 1 + x*A(2*x).
%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * k * 2^(k-1) * Stirling2(n,k) * a(k-1).
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^(i-j)*j*2^(j-1)*stirling(i, j, 2)*v[j])); v;
%Y Cf. A353177, A355093.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 20 2022
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