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 A318224 #8 Aug 21 2018 18:30:54
%S A318224 1,1,-3,37,-1007,47901,-3514499,367671697,-51952729023,9529552851193,
%T A318224 -2201241933756899,625136460673954461,-214066473170125310063,
%U A318224 86976878219664125966677,-41368038169392401671082787,22767783580493235411255966601,-14356419990032448099044028030719
%N A318224 a(n) = n! * [x^n] exp(x/(1 + n*x)).
%F A318224 a(n) = n! * [x^n] Product_{k>=1} exp((-n)^(k-1)*x^k).
%F A318224 a(n) = Sum_{k=0..n} (-n)^(n-k)*binomial(n-1,k-1)*n!/k!.
%F A318224 a(n) ~ -(-1)^n * c * n^(2*n - 1/2) / exp(n), where c = BesselJ(1,2) * sqrt(2*Pi) = 1.44563470980450699365002928132323794056211645203313522173628289... - _Vaclav Kotesovec_, Aug 21 2018
%t A318224 Table[n! SeriesCoefficient[Exp[x/(1 + n x)], {x, 0, n}], {n, 0, 16}]
%t A318224 Join[{1}, Table[Sum[(-n)^(n - k) Binomial[n - 1, k - 1] n!/k!, {k, n}], {n, 16}]]
%t A318224 Join[{1}, Table[(-1)^(n + 1) n^n (n - 1)! Hypergeometric1F1[1 - n, 2, 1/n], {n, 16}]]
%t A318224 Flatten[{1, Table[-(-1)^n * n^(n-1) * (n-1)! * LaguerreL[n-1, 1, 1/n], {n, 1, 20}]}] (* _Vaclav Kotesovec_, Aug 21 2018 *)
%Y A318224 Cf. A111884, A293146, A317279, A318223.
%K A318224 sign
%O A318224 0,3
%A A318224 _Ilya Gutkovskiy_, Aug 21 2018