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 A120259 #9 Apr 02 2021 08:19:34
%S A120259 1,2,4,11,46,302,3109,49345,1209058,45574112,2636237374,234854695297,
%T A120259 32081882854399,6733481882732516,2172532761103119601,
%U A120259 1074257501384373622001,816914977299535380309346,953227711986515337529688144,1706089496424625166250326935690
%N A120259 Row sums of number triangle A120258.
%H A120259 Alois P. Heinz, <a href="/A120259/b120259.txt">Table of n, a(n) for n = 0..103</a>
%F A120259 a(n) = sum{k=0..n, Product{j=0..k-1, C(2n-2k+j, n-k)/C(n-k+j, j)}}
%F A120259 Limit_{n->infinity} a(n)^(1/n^2) = r^(r/2) * (2-r)^(1 - r/2) = 1.238819877352130037160235229707224180528582190767293210626357503368..., where r = 0.370130616271672149875211085663371877443670059442239590157339853950... is the root of the equation (4 - 4*r)^(2 - 2*r) * r^r = (2-r)^(2-r). - _Vaclav Kotesovec_, Apr 02 2021
%t A120259 Table[Sum[Product[Binomial[2*n-2*k+j, n-k]/Binomial[n-k+j, j],{j,0,k-1}],{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Apr 02 2021 *)
%t A120259 Table[Sum[BarnesG[k+1] * BarnesG[n-k+1]^2 * BarnesG[2*n-k+1] / BarnesG[2*n-2*k+1], {k, 0, n}] / BarnesG[n+1]^2, {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 02 2021 *)
%Y A120259 Cf. A120258.
%K A120259 easy,nonn
%O A120259 0,2
%A A120259 _Paul Barry_, Jun 13 2006