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 A352292 #11 Mar 11 2022 08:32:22
%S A352292 1,2,11,91,1007,13941,231645,4490739,99496787,2480012329,68684121713,
%T A352292 2092433179431,69540117508119,2503694594140845,97076021030158565,
%U A352292 4032791843669289883,178701570260701316219,8413561430997560725713,419425619946011214516345
%N A352292 Expansion of e.g.f. 1/(2 - exp(x) - x/(1 - x)).
%F A352292 a(0) = 1; a(n) = Sum_{k=1..n} (k! + 1) * binomial(n,k) * a(n-k).
%t A352292 m = 18; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x/(1 - x)), {x, 0, m}], x] (* _Amiram Eldar_, Mar 11 2022 *)
%o A352292 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x/(1-x))))
%o A352292 (PARI) a(n) = if(n==0, 1, sum(k=1, n, (k!+1)*binomial(n, k)*a(n-k)));
%Y A352292 Cf. A002866, A352270, A352293.
%K A352292 nonn
%O A352292 0,2
%A A352292 _Seiichi Manyama_, Mar 11 2022