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 A335578 #7 Jan 27 2021 07:29:14
%S A335578 1,-1,-6,15,272,-745,-29976,61271,6065856,-2723697,-1941455080,
%T A335578 -3989345041,897021218400,4964061925511,-562221881675832,
%U A335578 -5689641396555705,456732442022509184,7321841133968133023,-464200472167634521800,-10961686347887871324289,573373115861405030522400
%N A335578 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * k^3 * a(n-k).
%F A335578 E.g.f.: 1 / (1 + exp(x) * x * (1 + 3*x + x^2)).
%F A335578 E.g.f.: 1 / (1 + Sum_{k>=1} k^3 * x^k / k!).
%t A335578 a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] k^3 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%t A335578 nmax = 20; CoefficientList[Series[1/(1 + Exp[x] x (1 + 3 x + x^2)), {x, 0, nmax}], x] Range[0, nmax]!
%Y A335578 Cf. A302397, A302870, A308862, A316088, A335577.
%K A335578 sign
%O A335578 0,3
%A A335578 _Ilya Gutkovskiy_, Jan 26 2021