This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351763 #20 Apr 26 2023 09:45:34
%S A351763 1,3,24,279,4332,84075,1958058,53202387,1652070696,57713665779,
%T A351763 2240196853710,95650311987483,4455281606078988,224815388384744859,
%U A351763 12216916158370619010,711312392929267383075,44176151714082889756368,2915038701200389804440675
%N A351763 Expansion of e.g.f. 1/(1 - 3*x*exp(x)).
%F A351763 E.g.f.: 1/(1 - 3*x*exp(x)).
%F A351763 a(n) = n! * Sum_{k=0..n} 3^(n-k) * (n-k)^k/k!.
%F A351763 a(0) = 1 and a(n) = 3 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
%F A351763 a(n) ~ n! / ((1 + LambertW(1/3)) * LambertW(1/3)^n). - _Vaclav Kotesovec_, Feb 19 2022
%o A351763 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*exp(x))))
%o A351763 (PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*(n-k)^k/k!);
%o A351763 (PARI) a(n) = if(n==0, 1, 3*n*sum(k=0, n-1, binomial(n-1, k)*a(k)));
%Y A351763 Column k=3 of A351761.
%Y A351763 Cf. A351778.
%K A351763 nonn
%O A351763 0,2
%A A351763 _Seiichi Manyama_, Feb 18 2022