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 A238696 #20 Oct 12 2021 14:00:03
%S A238696 1,1,2,21,497,18508,3297933,2348121769,2319121509374,4535739243360613,
%T A238696 58887253765506968848,1694438232474931034462251,
%U A238696 64598311562133275526222276162,8312693334404799592869803398802772,5827069387752679429926992257426553147833
%N A238696 a(n) = Sum_{k=0..floor(n/2)} binomial(n*(n-k), n*k).
%H A238696 G. C. Greubel, <a href="/A238696/b238696.txt">Table of n, a(n) for n = 0..69</a>
%H A238696 Vaclav Kotesovec, <a href="/A238696/a238696.jpg">Limits, graph for 500 terms</a>
%F A238696 Maximum is at k = n*(1-1/sqrt(5))/2 = 0.2763932... * n.
%F A238696 Limit n->infinity a(n)^(1/n^2) = (1+sqrt(5))/2.
%F A238696 Lim sup n->infinity a(n) / (5^(1/4)/(n*sqrt(2*Pi))*((1+sqrt(5))/2)^(n^2+1)) = JacobiTheta3(0,exp(-5*sqrt(5)/2)) = EllipticTheta[3,0,Exp[-5*Sqrt[5]/2]] = 1.007468786736926147579...
%F A238696 Lim inf n->infinity a(n) / (5^(1/4)/(n*sqrt(2*Pi))*((1+sqrt(5))/2)^(n^2+1)) = JacobiTheta2(0,exp(-5*sqrt(5)/2)) = EllipticTheta[2,0,Exp[-5*Sqrt[5]/2]] = 0.494414344263155315970...
%F A238696 a(n) = [x^(n^2)] (1-x)^(n-1)/((1-x)^n - x^(2*n)) for n > 0. - _Seiichi Manyama_, Oct 11 2021
%t A238696 Table[Sum[Binomial[n*(n-k), n*k], {k, 0, Floor[n/2]}], {n, 0, 20}]
%o A238696 (PARI) a(n)=sum(k=0,n\2, binomial(n*(n-k), n*k)) \\ _Charles R Greathouse IV_, Jul 29 2016
%Y A238696 Cf. A206849, A207136, A209331.
%K A238696 nonn,nice
%O A238696 0,3
%A A238696 _Vaclav Kotesovec_, Mar 03 2014