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 A354121 #25 Nov 19 2023 08:21:58
%S A354121 1,4,16,68,316,1616,9080,55800,373080,2699520,21035040,175708320,
%T A354121 1566916320,14862171840,149429426880,1587766126080,17779538050560,
%U A354121 209295747832320,2583920845209600,33389139008678400,450642388471395840,6342869733912760320
%N A354121 Expansion of e.g.f. 1/(1 - log(1 + x))^4.
%C A354121 a(46) is negative. - _Vaclav Kotesovec_, Jun 04 2022
%C A354121 It appears that a(n) is negative for even n >= 46. - _Felix Fröhlich_, Jun 04 2022
%H A354121 Vaclav Kotesovec, <a href="/A354121/b354121.txt">Table of n, a(n) for n = 0..450</a>
%F A354121 a(n) = (1/6) * Sum_{k=0..n} (k + 3)! * Stirling1(n,k).
%F A354121 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (3 * k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Nov 19 2023
%t A354121 Table[Sum[(k+3)! * StirlingS1[n,k], {k,0,n}]/6, {n,0,20}] (* _Vaclav Kotesovec_, Jun 04 2022 *)
%o A354121 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+x))^4))
%o A354121 (PARI) a(n) = sum(k=0, n, (k+3)!*stirling(n, k, 1))/6;
%Y A354121 Cf. A006252, A317280, A354120.
%Y A354121 Cf. A226738, A354123.
%K A354121 sign
%O A354121 0,2
%A A354121 _Seiichi Manyama_, May 17 2022