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 A368981 #13 Jan 13 2024 16:13:37
%S A368981 0,0,2,12,168,1720,33360,492324,12510848,242010864,7645282560,
%T A368981 183157788220,6930019734528,198083231524776,8738660263983104,
%U A368981 290276762478721620,14634486747811184640,554012204526293864416,31427811840457845964800,1335650409538235449288812,84210181959664202315202560
%N A368981 a(n) = Sum_{k=0..n} binomial(n, k - 1)*(1 - k)^(k - 1)*(n - k)*(n - k + 1)^(n - k).
%F A368981 Alternating row sums of A368849, negated.
%t A368981 A368981[n_] :=Sum[Binomial[n, k-1] If[k == 1, 1, (1-k)^(k-1)] (n-k) (n-k+1)^(n-k), {k, 0, n}];
%t A368981 Array[A368981, 25, 0] (* _Paolo Xausa_, Jan 13 2024 *)
%o A368981 (SageMath)
%o A368981 def a(n):
%o A368981 return sum(binomial(n, k-1)*(1 - k)^(k - 1)*(n - k)*(n - k + 1)^(n - k)
%o A368981 for k in range(n + 1))
%o A368981 print([a(n) for n in range(0, 21)])
%Y A368981 Cf. A368849.
%K A368981 nonn
%O A368981 0,3
%A A368981 _Peter Luschny_, Jan 11 2024