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 A351765 #16 Feb 19 2022 04:42:30
%S A351765 1,1,12,279,11536,746525,69768036,8902181575,1487939919936,
%T A351765 315597946293657,82839437215344100,26366747854082944451,
%U A351765 10006618140321691249296,4464690010732922712332149,2313871692128866349730705924,1378552938661073773617331110975
%N A351765 a(n) = n! * Sum_{k=0..n} n^(n-k) * (n-k)^k/k!.
%F A351765 a(n) = n! * [x^n] 1/(1 - n*x*exp(x)).
%F A351765 From _Vaclav Kotesovec_, Feb 19 2022: (Start)
%F A351765 a(n) ~ exp(1) * n! * n^n.
%F A351765 a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / exp(n-1). (End)
%t A351765 Join[{1}, Table[n!*Sum[n^(n - k)*(n - k)^k/k!, {k, 0, n}], {n, 1, 20}]] (* _Vaclav Kotesovec_, Feb 19 2022 *)
%o A351765 (PARI) a(n) = n!*sum(k=0, n, n^(n-k)*(n-k)^k/k!);
%Y A351765 Main diagonal of A351761.
%Y A351765 Cf. A332408, A351768, A351779.
%K A351765 nonn
%O A351765 0,3
%A A351765 _Seiichi Manyama_, Feb 18 2022