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

%I #9 Dec 25 2023 10:00:51

%S 1,0,4,29,351,5288,96844,2084787,51569293,1440778760,44860522140,

%T 1540040695961,57780774428299,2351977512750864,103224895866407236,

%U 4858737892917301679,244142543354321358297,13043294582176082455088,738250195765281754969108

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

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

%o (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+sum(j=1, i, 3^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A330149, A368451.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 24 2023