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 A368291 #9 Feb 27 2025 17:21:42
%S A368291 1,2,9,64,601,7046,99169,1628404,30558609,645145642,15133509721,
%T A368291 390493864520,10992015298345,335198866337518,11008101913855089,
%U A368291 387333950619801916,14537422513124682913,579719887191660443858,24477810534426983873833
%N A368291 Expansion of e.g.f. exp(x) / (1 - x*exp(2*x)).
%F A368291 a(n) = n! * Sum_{k=0..n} (2*(n-k)+1)^k / k!.
%t A368291 With[{nn=20},CoefficientList[Series[Exp[x]/(1-x Exp[2x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 27 2025 *)
%o A368291 (PARI) a(n) = n!*sum(k=0, n, (2*(n-k)+1)^k/k!);
%Y A368291 Cf. A368292.
%K A368291 nonn,easy
%O A368291 0,2
%A A368291 _Seiichi Manyama_, Dec 19 2023