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 A335111 #10 May 20 2023 07:29:08
%S A335111 0,1,-2,6,-8,40,48,784,5248,49536,490240,5403904,64822272,842742784,
%T A335111 11798284288,176974510080,2831591636992,48137058942976,
%U A335111 866467058614272,16462874118651904,329257482362552320,6914407129635618816,152116956851937476608,3498690007594658430976
%N A335111 a(n) = n! * Sum_{k=0..n-1} (-2)^k / k!.
%C A335111 Inverse binomial transform of A000240.
%F A335111 G.f.: Sum_{k>=1} k! * x^k / (1 + 2*x)^(k + 1).
%F A335111 E.g.f.: x*exp(-2*x) / (1 - x).
%F A335111 a(n) = A000023(n) - A122803(n).
%F A335111 a(n) ~ exp(-2) * n!. - _Vaclav Kotesovec_, Jun 08 2022
%F A335111 a(n) = Sum_{k=0..n} (-1)^k * k * A008290(n,k). - _Alois P. Heinz_, May 20 2023
%t A335111 Table[n! Sum[(-2)^k/k!, {k, 0, n - 1}], {n, 0, 23}]
%t A335111 nmax = 23; CoefficientList[Series[Sum[k! x^k/(1 + 2 x)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x]
%t A335111 nmax = 23; CoefficientList[Series[x Exp[-2 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%o A335111 (PARI) a(n) = n! * sum(k=0, n-1, (-2)^k / k!); \\ _Michel Marcus_, May 23 2020
%Y A335111 Cf. A000023, A000240, A008290, A066534, A087981, A122803.
%K A335111 sign
%O A335111 0,3
%A A335111 _Ilya Gutkovskiy_, May 23 2020