%I #9 Jun 19 2022 09:43:18
%S 1,3,15,87,414,-333,-36207,-125415,9692208,65346480,-6686193834,
%T -28979410023,9399236141664,-74034590428035,-21601690453093869,
%U 753341807730002715,64208547156310265880,-6137571162315494165580,-131200755856066508312736
%N E.g.f. A(x) satisfies A(x) = 1 + 3 * log(1+x) * A(log(1+x)).
%F E.g.f. A(x) satisfies: A(exp(x) - 1) = 1 + 3*x*A(x).
%F a(0) = 1; a(n) = 3 * Sum_{k=1..n} k * 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]=3*sum(j=1, i, j*stirling(i, j, 1)*v[j])); v;
%Y Cf. A354728, A355096.
%Y Cf. A355105.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jun 19 2022