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 A352307 #12 Mar 12 2022 11:15:20
%S A352307 1,1,3,14,83,621,5583,58493,700507,9438253,141291843,2326680313,
%T A352307 41797029035,813422096709,17047913249279,382815685896293,
%U A352307 9169316015977675,233352842701661021,6288004372005738747,178851946015229702545,5354894260179239755995
%N A352307 Expansion of e.g.f. 1/(2 - exp(x) - x^3/6).
%F A352307 a(n) = binomial(n,3) * a(n-3) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.
%t A352307 m = 20; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^3/6), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352307 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^3/6)))
%o A352307 (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m))*binomial(n, k)*b(n-k, m)));
%o A352307 a(n) = b(n, 3);
%Y A352307 Cf. A006155, A352306, A352308.
%Y A352307 Cf. A352299.
%K A352307 nonn
%O A352307 0,3
%A A352307 _Seiichi Manyama_, Mar 11 2022