%I #8 Jun 18 2022 23:03:51
%S 1,1,5,128,13572,5462934,7948602294,40533916402440,709019302729063320,
%T 41863690463023189162224,8239820880700969013925719856,
%U 5352039696398504114334881521575792,11377141201027327036487229661596883688304
%N E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(3*x).
%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * 3^(n-k) * (k-1)! * binomial(n,k) * a(n-k).
%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)^(j-1)*3^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
%Y Cf. A006252, A355084.
%Y Cf. A355087, A355088.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 18 2022