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%I #7 Dec 02 2023 13:18:23
%S 1,4,41,654,14028,377112,12177126,458916588,19769059944,958125646080,
%T 51597765220608,3056601306206016,197532472461453072,
%U 13829353660386169344,1042679226974498229456,84229294995413626072608,7257792124889497549663488
%N Expansion of e.g.f. 1/(1 - x + log(1 - 3*x)).
%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 3^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]=i*v[i]+sum(j=1, i, 3^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
%Y Cf. A052820, A367845, A367847.
%Y Cf. A367836.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Dec 02 2023
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