%I #15 Jun 04 2022 02:37:29

%S 1,3,21,222,3132,55242,1169262,28873800,814870584,25871762016,

%T 912684973968,35416732159872,1499286521185776,68757945743286576,

%U 3395829155786528976,179693346163010491008,10142543588881013369856,608262031900883147262336

%N Expansion of e.g.f. 1/(1 + 3 * log(1-x)).

%F a(0) = 1; a(n) = 3 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).

%F a(n) = Sum_{k=0..n} 3^k * k! * |Stirling1(n, k)|.

%F a(n) ~ n! * exp(n/3) / (3 * (exp(1/3) - 1)^(n+1)). - _Vaclav Kotesovec_, Jun 04 2022

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*log(1-x))))

%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-1)!*binomial(i, j)*v[i-j+1])); v;

%o (PARI) a(n) = sum(k=0, n, 3^k*k!*abs(stirling(n, k, 1)));

%Y Column k=3 of A320079.

%Y Cf. A335531.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 21 2022