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 A352300 #16 Mar 12 2022 07:54:24
%S A352300 1,1,3,13,99,781,7563,84253,1103595,16074589,260443083,4630046653,
%T A352300 90017588235,1894771249021,42957132108075,1043136555486493,
%U A352300 27024421701469995,743851294350730141,21679544916491784843,666932347454809048189
%N A352300 Expansion of e.g.f. 1/(2 - exp(x) - x^4).
%F A352300 a(n) = n * (n-1) * (n-2) * (n-3) * a(n-4) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 3.
%t A352300 m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^4), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352300 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^4)))
%o A352300 (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
%o A352300 a(n) = b(n, 4);
%Y A352300 Cf. A006155, A346269, A352299.
%Y A352300 Cf. A352304.
%K A352300 nonn
%O A352300 0,3
%A A352300 _Seiichi Manyama_, Mar 11 2022