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 A368266 #10 Feb 21 2025 16:56:16
%S A368266 1,-1,4,1,60,393,4498,54689,773384,12268369,216328614,4195769433,
%T A368266 88776964444,2034936319817,50232646818890,1328570248040497,
%U A368266 37481046375146640,1123486426007081505,35657224567565828302,1194561018775753556777,42125545306641497600036
%N A368266 Expansion of e.g.f. exp(-2*x) / (1 - x*exp(x)).
%F A368266 a(n) = n! * Sum_{k=0..n} (n-k-2)^k / k!.
%t A368266 CoefficientList[Series[Exp[-2*x]/ (1 - x*Exp[x]),{x,0,20}],x]Range[0,20]! (* _Stefano Spezia_, Feb 21 2025 *)
%o A368266 (PARI) a(n) = n!*sum(k=0, n, (n-k-2)^k/k!);
%Y A368266 Cf. A006153, A072597, A092148, A368265.
%K A368266 sign,easy
%O A368266 0,3
%A A368266 _Seiichi Manyama_, Dec 19 2023