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 A330497 #19 Sep 08 2022 08:46:24
%S A330497 1,0,1,26,1089,70124,6495985,821315214,136115947009,28651724077976,
%T A330497 7470040450004001,2363470644596843330,892244303052345224641,
%U A330497 396227360441775922668036,204487588996059177697597969,121370399839482643287189048374
%N A330497 a(n) = n! * Sum_{k=0..n} (-1)^k * binomial(n,k) * n^(n - k) / k!.
%F A330497 a(n) = n! * [x^n] exp(-x/(1 - n*x)) / (1 - n*x).
%F A330497 a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k)^2 * n^k * k!.
%F A330497 a(n) ~ sqrt(2*Pi) * BesselJ(0,2) * n^(2*n + 1/2) / exp(n). - _Vaclav Kotesovec_, Dec 18 2019
%t A330497 Join[{1}, Table[n! Sum[(-1)^k Binomial[n, k] n^(n - k)/k!, {k, 0, n}], {n, 1, 15}]]
%t A330497 Join[{1}, Table[n^n n! LaguerreL[n, 1/n], {n, 1, 15}]]
%t A330497 Table[n! SeriesCoefficient[Exp[-x/(1 - n x)]/(1 - n x), {x, 0, n}], {n, 0, 15}]
%o A330497 (Magma) [Factorial(n)*&+[(-1)^k*Binomial(n,k)*n^(n-k)/Factorial(k):k in [0..n]]:n in [0..15]]; // _Marius A. Burtea_, Dec 18 2019
%Y A330497 Cf. A009940, A025166, A061711, A277423, A307885, A318224, A319392, A330260.
%K A330497 nonn
%O A330497 0,4
%A A330497 _Ilya Gutkovskiy_, Dec 18 2019