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 A351778 #15 May 21 2024 13:22:51
%S A351778 1,-3,12,-63,420,-3435,33462,-379155,4903896,-71318259,1152202290,
%T A351778 -20474486043,396890715636,-8334602179995,188486823883134,
%U A351778 -4567087352339235,118039115079323952,-3241465018561379427,94249758656850366186,-2892678859033260044043
%N A351778 Expansion of e.g.f. 1/(1 + 3*x*exp(x)).
%F A351778 a(n) = n! * Sum_{k=0..n} (-3)^(n-k) * (n-k)^k/k!.
%F A351778 a(0) = 1 and a(n) = -3 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
%t A351778 With[{nn=30},CoefficientList[Series[1/(1+3x Exp[x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 21 2024 *)
%o A351778 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*exp(x))))
%o A351778 (PARI) a(n) = n!*sum(k=0, n, (-3)^(n-k)*(n-k)^k/k!);
%o A351778 (PARI) a(n) = if(n==0, 1, -3*n*sum(k=0, n-1, binomial(n-1, k)*a(k)));
%Y A351778 Column k=3 of A351776.
%Y A351778 Cf. A351763.
%K A351778 sign
%O A351778 0,2
%A A351778 _Seiichi Manyama_, Feb 19 2022