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 A367272 #7 Nov 12 2023 07:51:18
%S A367272 1,1,5,28,209,1826,18217,203106,2487361,33077566,473318201,7234847126,
%T A367272 117435618577,2014339775800,36360190887217,688237505878726,
%U A367272 13618646813974785,280960214041690038,6028928694559721305,134277542969681115870,3098232871805383942801
%N A367272 a(n) = Sum_{k=0..n} binomial(n, k)^2 * k^(n - k).
%F A367272 a(n) = Sum_{k=0..n} binomial(n, k) * A059297(n, k).
%F A367272 log(a(n)) ~ n*(log(n) - log(log(n)) - 1 + (3*log(log(n)) + 2)/log(n) - 1/log(n)^2). - _Vaclav Kotesovec_, Nov 12 2023
%p A367272 a := n -> add(binomial(n, k)^2*k^(n - k), k = 0 .. n):
%p A367272 seq(a(n), n = 0..22);
%t A367272 Join[{1}, Table[Sum[Binomial[n,k]^2 * k^(n-k), {k, 0, n}], {n, 1, 20}]] (* _Vaclav Kotesovec_, Nov 12 2023 *)
%Y A367272 Cf. A059297.
%K A367272 nonn
%O A367272 0,3
%A A367272 _Peter Luschny_, Nov 11 2023