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%I #6 Dec 20 2023 12:37:05
%S 1,2,11,97,1109,15821,271255,5425967,124032137,3189663433,91141189931,
%T 2864686414547,98226339773677,3648723468367277,145961603607355775,
%U 6256040115149251591,286015221831125756945,13893373399551594686609,714578347872583574806099
%N Expansion of e.g.f. exp(x) / (1 - x*exp(3*x)).
%F a(n) = n! * Sum_{k=0..n} (3*(n-k)+1)^k / k!.
%o (PARI) a(n) = n!*sum(k=0, n, (3*(n-k)+1)^k/k!);
%Y Cf. A336948, A368293.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Dec 19 2023
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