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 A346269 #28 Apr 17 2022 20:53:06
%S A346269 1,1,5,25,195,1781,20043,260317,3881083,64978861,1209674883,
%T A346269 24764370533,553130762451,13383468009445,348741065652619,
%U A346269 9736370899180813,289948812396124875,9174320178178480829,307362076657095903411,10869452423023391315413,404614540610985119535715
%N A346269 Expansion of e.g.f. 1/(2 - x^2 - exp(x)).
%H A346269 Seiichi Manyama, <a href="/A346269/b346269.txt">Table of n, a(n) for n = 0..408</a>
%F A346269 E.g.f.: 1/(2 - x^2 - exp(x)).
%F A346269 a(n) ~ n! / ((2 + 2*r - r^2) * r^(n+1)), where r = A201752 = 0.5372744491738566... is the positive root of the equation 2 - r^2 - exp(r) = 0.
%F A346269 a(0) = a(1) = 1; a(n) = n * (n-1) * a(n-2) + Sum_{k=1..n} binomial(n,k) * a(n-k). - _Seiichi Manyama_, Mar 11 2022
%t A346269 nmax = 20; CoefficientList[Normal[Series[1/(2-x^2-E^x), {x, 0, nmax}]], x] * Range[0, nmax]!
%o A346269 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(2 - x^2 - exp(x)))) \\ _Michel Marcus_, Jul 12 2021
%o A346269 (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
%o A346269 a(n) = b(n, 2); \\ _Seiichi Manyama_, Mar 12 2022
%Y A346269 Cf. A006155, A201752.
%K A346269 nonn
%O A346269 0,3
%A A346269 _Vaclav Kotesovec_, Jul 12 2021