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

%I #9 Dec 25 2023 10:01:50

%S 1,4,34,469,8815,208348,5922118,196568419,7459854973,318560689324,

%T 15116763184978,789119869380577,44939583072146251,2772582488089509028,

%U 184216538154508055062,13114092114632287359919,995813104288130697683065,80342826520464644566291828

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

%F 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)); for(i=0, n, v[i+1]=1+sum(j=1, i, 3^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A291979, A368444.

%Y Cf. A343709.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 24 2023