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 A335577 #8 Jan 27 2021 07:29:09
%S A335577 1,-1,-2,9,32,-285,-1236,18725,86176,-2087001,-9204580,351964569,
%T A335577 1336442304,-83422970917,-231889447076,26389118293005,35917342192064,
%U A335577 -10722110983670193,5028963509133756,5432569724760331841,-14852185163192897120,-3352369390318855889661
%N A335577 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * k^2 * a(n-k).
%F A335577 E.g.f.: 1 / (1 + exp(x) * x * (1 + x)).
%F A335577 E.g.f.: 1 / (1 + Sum_{k>=1} k^2 * x^k / k!).
%t A335577 a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] k^2 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
%t A335577 nmax = 21; CoefficientList[Series[1/(1 + Exp[x] x (1 + x)), {x, 0, nmax}], x] Range[0, nmax]!
%Y A335577 Cf. A302189, A302397, A308861, A316087, A335578.
%K A335577 sign
%O A335577 0,3
%A A335577 _Ilya Gutkovskiy_, Jan 26 2021