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 A369071 #13 Jan 28 2024 18:07:00
%S A369071 0,1,6,57,712,10905,197136,4102777,96552576,2534382513,73397843200,
%T A369071 2324613341721,79923267523584,2964436169152393,117986961509824512,
%U A369071 5015721009078977625,226816401312675168256,10871698383944129824353,550571805478900954497024
%N A369071 a(n) = Sum_{k=0..n} binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k).
%p A369071 A369071 := n -> local k; add(binomial(n, k-1)*(k-1)^(k-1)*k*(n-k+1)^(n-k), k=0..n): seq(A369071(n), n = 0..18);
%t A369071 A369071[n_] := Sum[Binomial[n, k-1] If[k == 1, 1, (k-1)^(k-1)] k (n-k+1)^(n-k), {k, n}]; Array[A369071, 20, 0] (* _Paolo Xausa_, Jan 28 2024 *)
%o A369071 (SageMath)
%o A369071 def A369071(n):
%o A369071 return sum(binomial(n, k - 1)*(k - 1)^(k - 1)*k*(n - k + 1)^(n - k)
%o A369071 for k in range(n + 1))
%o A369071 print([A369071(n) for n in range(11)])
%Y A369071 Cf. Row sums of A369019.
%K A369071 nonn
%O A369071 0,3
%A A369071 _Peter Luschny_, Jan 13 2024