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 A343032 #20 Apr 04 2021 00:49:39
%S A343032 1,2,4,9,24,78,313,1557,9606,73482,696736,8187149,119214337,
%T A343032 2150935400,48085463503,1331903411529,45708405952786,1943464419169294,
%U A343032 102378212255343442,6681679619583450775,540264005909352759970,54120992439329583459008,6716802027097934788929023
%N A343032 Row sums of triangle A073165.
%F A343032 a(n) = Sum_{k=0..n} Product_{1<=i<=j<=k} (n-k+i+j-1)/(i+j-1).
%F A343032 Limit_{n->infinity} a(n)^(1/n^2) = 2^r * r^(r/2) * (1-r)^((1-r)/2) = 1.113022855718664043805172905388731078607920794227951582456470883692074109..., where r = 0.62986938372832785012478891433662812255632994055776040984266... is the root of the equation 2^(4*r) * (1-r)^(1-r) * r^(2*r) = (1+r)^(1+r). - _Vaclav Kotesovec_, Apr 03 2021
%t A343032 Table[Sum[Product[(n - k + i + j - 1)/(i + j - 1), {i, 1, k}, {j, 1, i}], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 03 2021 *)
%t A343032 Table[Sum[BarnesG[k+1] / BarnesG[n+1] * Sqrt[Gamma[k+1] * Gamma[(n-k+2)/2] * BarnesG[n-k+1] * BarnesG[n+k+2] / (Gamma[n-k+1] * Gamma[(n+k+2)/2] * BarnesG[2*k+2])], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 03 2021 *)
%o A343032 (PARI) a(n) = sum(k=0, n, prod(i=1, k, prod(j=1, i, (n-k+i+j-1)/(i+j-1))));
%Y A343032 Cf. A073165, A120259.
%K A343032 nonn
%O A343032 0,2
%A A343032 _Seiichi Manyama_, Apr 03 2021