%I #9 Jun 20 2022 08:36:15
%S 1,1,5,74,2778,248244,51212444,23984832416,25218677193200,
%T 59000757443457072,304720138059811544048,3449059394896458379058208,
%U 84991203371449537414272981856,4532232538284485346856696552505728,520204832574009673696495358635072488576
%N E.g.f. A(x) satisfies A(x) = 1 - log(1-x) * A(-2 * log(1-x)).
%F E.g.f. A(x) satisfies: A(1 - exp(-x)) = 1 + x*A(2*x).
%F a(0) = 1; a(n) = Sum_{k=1..n} k * 2^(k-1) * |Stirling1(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, j*2^(j-1)*abs(stirling(i, j, 1))*v[j])); v;
%Y Cf. A135750, A355086, A355098.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 20 2022