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 A352293 #15 Jul 25 2022 03:10:46
%S A352293 1,2,7,43,335,3301,38925,535851,8429139,149173321,2933274593,
%T A352293 63446532271,1497102036567,38269877372637,1053531222709269,
%U A352293 31074273060116083,977649690943993979,32680936703516606737,1156722832021068313833,43216064601701505904983
%N A352293 Expansion of e.g.f. 1/(2 - exp(x) - x/(1 + x)).
%H A352293 Vaclav Kotesovec, <a href="/A352293/b352293.txt">Table of n, a(n) for n = 0..400</a>
%F A352293 a(0) = 1; a(n) = Sum_{k=1..n} ((-1)^(k-1) * k! + 1) * binomial(n,k) * a(n-k).
%F A352293 a(n) ~ n! * (1+r)^2 / ((3 + r*(3+r)) * r^(n+1)), where r = 0.50855472406037552... is the root of the equation 2 - exp(r) - r/(1+r) = 0. - _Vaclav Kotesovec_, Jul 25 2022
%t A352293 m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x/(1 + x)), {x, 0, m}], x] (* _Amiram Eldar_, Mar 11 2022 *)
%o A352293 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x/(1+x))))
%o A352293 (PARI) a(n) = if(n==0, 1, sum(k=1, n, ((-1)^(k-1)*k!+1)*binomial(n, k)*a(n-k)));
%Y A352293 Cf. A006155, A352271, A352292.
%K A352293 nonn
%O A352293 0,2
%A A352293 _Seiichi Manyama_, Mar 11 2022