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 A209428 #13 Jan 27 2019 06:16:51
%S A209428 1,1,2,5,29,284,4423,146913,12314170,1881868883,442540106327,
%T A209428 198351607585964,242843144659704443,641109494638274737567,
%U A209428 2641514784666925880476348,17914201815999230497003603969,302266027138470510426936352722523
%N A209428 a(n) = Sum_{k=0..[n/2]} binomial(n-k,k)^(n-k).
%C A209428 Equals antidiagonal sums of triangle A209427.
%H A209428 G. C. Greubel, <a href="/A209428/b209428.txt">Table of n, a(n) for n = 0..82</a>
%F A209428 Limit n->infinity a(n)^(1/n^2) = ((1-r)/r)^((1-r)^2/(3-4*r)) = 1.4360944969025357119535113523184471..., where r = A323777 = 0.220676041323740696312822269998... is the root of the equation (1-2*r)^(3-4*r) = (1-r)^(2-2*r) * r^(1-2*r). - _Vaclav Kotesovec_, Mar 06 2014
%t A209428 Table[Sum[Binomial[n-k,k]^(n-k),{k,0,Floor[n/2]}],{n,0,20}] (* _Vaclav Kotesovec_, Mar 06 2014 *)
%o A209428 (PARI) {a(n)=sum(k=0,n\2,binomial(n-k,k)^(n-k))}
%o A209428 for(n=0,20,print1(a(n),", "))
%Y A209428 Cf. A209427, A209331.
%K A209428 nonn
%O A209428 0,3
%A A209428 _Paul D. Hanna_, Mar 08 2012