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 A352306 #14 Mar 12 2022 11:15:30
%S A352306 1,1,4,19,129,1071,10743,125455,1675439,25167073,420070323,7712503173,
%T A352306 154475622513,3351859639363,78324320723561,1960968388497523,
%U A352306 52368881358012435,1485952518531483045,44643697199669589447,1415782273405809697009
%N A352306 Expansion of e.g.f. 1/(2 - exp(x) - x^2/2).
%F A352306 a(n) = binomial(n,2) * a(n-2) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 1.
%t A352306 m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^2/2), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352306 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^2/2)))
%o A352306 (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m))*binomial(n, k)*b(n-k, m)));
%o A352306 a(n) = b(n, 2);
%Y A352306 Cf. A006155, A352307, A352308.
%Y A352306 Cf. A346269, A352309.
%K A352306 nonn
%O A352306 0,3
%A A352306 _Seiichi Manyama_, Mar 11 2022