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 A384200 #15 May 22 2025 16:41:58
%S A384200 0,1,5,33,294,3414,49644,872388,18001584,426553776,11408104800,
%T A384200 339766164000,11148335337600,399489448694400,15520734764640000,
%U A384200 649782085752172800,29160211264750540800,1396381090351116441600,71068392067688315596800,3830710201119961857331200
%N A384200 Expansion of e.g.f. -log(1 - 3*x)/(3 * (1 - x)).
%H A384200 Vincenzo Librandi, <a href="/A384200/b384200.txt">Table of n, a(n) for n = 0..200</a>
%F A384200 a(n) = n! * Sum_{k=1..n} 3^(k-1)/k.
%F A384200 a(n) = n * a(n-1) + 3^(n-1) * (n-1)!.
%F A384200 a(n) = (4*n-3) * a(n-1) - 3 * (n-1)^2 * a(n-2).
%t A384200 a[n_]:= n! * Sum[(3)^(k-1)/k,{k,1,n}];Table[a[n],{n,0,19}] (* _Vincenzo Librandi_, May 22 2025 *)
%o A384200 (PARI) a(n) = n!*sum(k=1, n, 3^(k-1)/k);
%o A384200 (Magma) [0] cat [n le 1 select 1 else n * Self(n-1) + 3^(n-1) * Factorial(n-1): n in [1..20]]; // _Vincenzo Librandi_, May 22 2025
%Y A384200 Cf. A126674.
%K A384200 nonn,easy
%O A384200 0,3
%A A384200 _Seiichi Manyama_, May 22 2025