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 A354018 #22 Jun 02 2025 15:25:17
%S A354018 0,1,3,20,172,1864,24248,368136,6388128,124711944,2705241672,
%T A354018 64550432352,1680280323984,47383464508080,1438986494794704,
%U A354018 46821994627363968,1625069178022566528,59927028756823323648,2339899614887520358656,96439023491479275172608
%N A354018 Expansion of e.g.f. -log(1-x)/(1 + log(1-x) - log(1-x)^2).
%F A354018 a(n) = Sum_{k=0..n} k! * Fibonacci(k) * |Stirling1(n,k)|.
%F A354018 a(n) ~ n! * (sqrt(5) - 1) / (2 * sqrt(5) * exp((sqrt(5) - 1)/2) * (1 - exp((1 - sqrt(5))/2))^(n+1)). - _Vaclav Kotesovec_, May 15 2022
%t A354018 Table[Sum[k! * Fibonacci[k] * Abs[StirlingS1[n,k]], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, May 15 2022 *)
%t A354018 With[{nn=20},CoefficientList[Series[-Log[1-x]/(1+Log[1-x]-Log[1-x]^2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 22 2024 *)
%o A354018 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-log(1-x)/(1+log(1-x)-log(1-x)^2))))
%o A354018 (PARI) a(n) = sum(k=0, n, k!*fibonacci(k)*abs(stirling(n, k, 1)));
%Y A354018 Cf. A000045, A005444, A005445, A265165, A320352, A354013.
%K A354018 nonn
%O A354018 0,3
%A A354018 _Seiichi Manyama_, May 14 2022