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 A352299 #17 Mar 12 2022 11:15:42
%S A352299 1,1,3,19,123,1021,10683,127093,1725867,26535613,452307243,8475606613,
%T A352299 173390108235,3842119808749,91675559886459,2343875745873493,
%U A352299 63920729617231275,1852126733351677021,56823327291638414667,1840195730889731550805
%N A352299 Expansion of e.g.f. 1/(2 - exp(x) - x^3).
%F A352299 a(n) = n * (n-1) * (n-2) * a(n-3) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.
%t A352299 m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^3), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352299 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^3)))
%o A352299 (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
%o A352299 a(n) = b(n, 3);
%Y A352299 Cf. A006155, A346269, A352300.
%Y A352299 Cf. A352303, A352307.
%K A352299 nonn
%O A352299 0,3
%A A352299 _Seiichi Manyama_, Mar 11 2022