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 A384199 #18 May 23 2025 03:28:59
%S A384199 0,1,5,47,558,8394,150972,3171132,76102128,2054797776,61643570400,
%T A384199 2034241452000,73232652355200,2856073920854400,119955098448864000,
%U A384199 5397979517377171200,259103015526429849600,13214253812770712217600,713569705533931031654400
%N A384199 Expansion of e.g.f. log(1 + x)/(1 - 3*x).
%H A384199 Vincenzo Librandi, <a href="/A384199/b384199.txt">Table of n, a(n) for n = 0..200</a>
%F A384199 a(n) = n! * Sum_{k=1..n} (-1)^(k-1) * 3^(n-k)/k.
%F A384199 a(n) = 3 * n * a(n-1) - (-1)^n * (n-1)!.
%F A384199 a(n) = (2*n+1) * a(n-1) + 3 * (n-1)^2 * a(n-2).
%F A384199 a(n) ~ log(4/3) * 3^n * n!. - _Vaclav Kotesovec_, May 23 2025
%t A384199 a[n_]:= n! * Sum[(-1)^(k-1)*3^(n-k)/k,{k,1,n}];Table[a[n],{n,0,18}] (* _Vincenzo Librandi_, May 22 2025 *)
%o A384199 (PARI) a(n) = n!*sum(k=1, n, (-1)^(k-1)*3^(n-k)/k);
%o A384199 (Magma) [0] cat [n le 1 select 1 else 3 * n * Self(n-1) - (-1)^n * Factorial(n-1): n in [1..20]]; // _Vincenzo Librandi_, May 22 2025
%Y A384199 Cf. A024167, A383897.
%Y A384199 Cf. A069015.
%K A384199 nonn,easy
%O A384199 0,3
%A A384199 _Seiichi Manyama_, May 22 2025