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%I #11 Jun 20 2022 08:36:35
%S 1,1,4,42,1160,83270,14923212,6414048354,6410464368912,
%T 14565079937500542,73986188807621474900,829702542906852010728090,
%U 20340869993779258576653846936,1081654382501102944417336793863094,123961854316018592747078219803021082332
%N E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (1 - exp(-x))).
%F a(0) = 1; a(n) = n * Sum_{k=0..n-1} (-1)^(n-k-1) * 2^k * Stirling2(n-1,k) * a(k).
%F a(n) = n * A355132(n-1) for n>0.
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*sum(j=0, i-1, (-1)^(i-j-1)*2^j*stirling(i-1, j, 2)*v[j+1])); v;
%Y Cf. A354574, A355102, A355132.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 20 2022
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