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 A346200 #4 Jul 10 2021 09:04:52
%S A346200 1,3,43,8913,26762121,1173960290163,786113240166904651,
%T A346200 8613513810086378347343577,1711294617015624229036545787666921,
%U A346200 6770959866814792643630677926543098580902523,536479956775359246458147222888630941089874512707772963
%N A346200 a(n) = Sum_{k=0..n} (binomial(n+k,k) * binomial(n,k))^k.
%F A346200 a(n)^(1/n) ~ (1+r)^(r*n/2 - 1/4) / ((2*Pi*n)^r * (1-r)^(r*n/2 + r - 1/4)), where r = 0.9222727963503830123185148157257918806196371551687495361664171679710425... is the root of the equation (1-r)^(2*r-1) * (1+r)^(2*r+1) = r^(4*r).
%t A346200 Table[Sum[(Binomial[n+k, k]*Binomial[n, k])^k, {k, 0, n}], {n, 0, 12}]
%Y A346200 Cf. A336873.
%K A346200 nonn
%O A346200 0,2
%A A346200 _Vaclav Kotesovec_, Jul 10 2021