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 A228837 #16 Jan 05 2018 22:00:44
%S A228837 1,1,2,5,38,597,14472,554653,44421258,8933194659,3408672951784,
%T A228837 1984802013951149,1803179670478111304,3323206887194925488269,
%U A228837 15156709454119350064982141,132889643918499982093215167857,1784438297905511051093397284187186
%N A228837 a(n) = Sum_{k=0..[n/2]} binomial((n-k)^2, (n-2*k)*k).
%C A228837 Equals the antidiagonal sums of triangle A228836.
%H A228837 G. C. Greubel, <a href="/A228837/b228837.txt">Table of n, a(n) for n = 0..86</a>
%F A228837 Limit n->infinity a(n)^(1/n^2) = ((1-r)^2/(r*(1-2*r)))^((1-3*r)*(1-r)/(3*(1-2*r))) = 1.36198508972775011599..., where r = 0.195220321930105755... is the root of the equation (1-3*r+3*r^2)^(3*(2*r-1)) = (r*(1-2*r))^(4*r-1) * (1-r)^(4*(r-1)). - _Vaclav Kotesovec_, added Sep 05 2013, simplified Mar 04 2014
%t A228837 Table[Sum[Binomial[(n-k)^2, (n-2*k)*k],{k,0,Floor[n/2]}],{n,0,15}] (* _Vaclav Kotesovec_, Sep 05 2013 *)
%o A228837 (PARI) {a(n)=sum(k=0,n\2,binomial((n-k)^2, (n-2*k)*k))}
%o A228837 for(n=0,30,print1(a(n),", "))
%Y A228837 Cf. A228836, A207138.
%Y A228837 Cf. variants: A209331, A228833, A123165.
%K A228837 nonn
%O A228837 0,3
%A A228837 _Paul D. Hanna_, Sep 05 2013