%I #41 Jun 05 2022 00:44:14
%S 1,1,1,-2,-13,61,612,-8924,-41991,2821876,-22689807,-1196339088,
%T 45175812442,10968806278,-63633205318330,2495113782094766,
%U 31372553334367367,-8832192422722410665,421480840601004167822,9536361803340658184343
%N E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(1 - exp(-x)).
%F E.g.f. A(x) satisfies: A(-log(1-x)) = 1 + x*A(x).
%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n-k) * k * 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*stirling(i, j, 2)*v[j])); v;
%Y Cf. A135750, A213357, A354574, A354728, A354730.
%K sign
%O 0,4
%A _Seiichi Manyama_, Jun 04 2022