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 A350268 #8 Dec 25 2021 14:51:48
%S A350268 1,1,4,22,168,1720,22670,368784,7134148,159416704,4027395330,
%T A350268 113235212800,3501763366904,118024658758656,4303855119215782,
%U A350268 168777440194263040,7081468496171815500,316501174908316647424,15010862087643791689322,752916261526858377363456
%N A350268 a(n) = Sum_{k=0..n} (n - k)! * (n - 1)^k. Row sums of A350269.
%t A350268 a[1] = 1; a[n_] := Sum[(n - k)! * (n - 1)^k, {k, 0, n}]; Array[a, 20, 0] (* _Amiram Eldar_, Dec 25 2021 *)
%o A350268 (PARI) a(n) = sum(k=0, n, (n-k)!*(n-1)^k); \\ _Michel Marcus_, Dec 25 2021
%Y A350268 Cf. A350269.
%K A350268 nonn
%O A350268 0,3
%A A350268 _Peter Luschny_, Dec 25 2021