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 A379992 #12 Jun 14 2025 13:06:56
%S A379992 1,1,7,41,349,3539,42451,585605,9130297,158692679,3041499871,
%T A379992 63712004729,1447946191957,35479218963083,932326476195115,
%U A379992 26153289728300909,779995883104560241,24644267406802467215,822278654588440803511,28891372907012629446881
%N A379992 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^2.
%F A379992 a(n) = n! * Sum_{k=0..n} (k+1) * (k-1)^(n-k)/(n-k)!.
%t A379992 With[{nn=20},CoefficientList[Series[Exp[-3x]/(Exp[-x]-x)^2,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jun 14 2025 *)
%o A379992 (PARI) a(n) = n!*sum(k=0, n, (k+1)*(k-1)^(n-k)/(n-k)!);
%Y A379992 Cf. A358738, A377529, A379933, A379997.
%Y A379992 Cf. A368266, A377530, A379994.
%K A379992 nonn,easy
%O A379992 0,3
%A A379992 _Seiichi Manyama_, Jan 07 2025