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 A332231 #29 Feb 09 2020 02:45:02
%S A332231 1,2,30,924,41990,2521260,188296108,16825310040,1750702260294,
%T A332231 207921866100300,27755558583300548,4114068719809705800,
%U A332231 670456479908731386780,119149476568133242798840,22932161636278362035091480
%N A332231 a(n) = 1/n! * ((n+1)*n)!/Gamma(1 + (n+1)*n/2) * Gamma(1 + (n-1)*n/2)/((n-1)*n)!.
%H A332231 Seiichi Manyama, <a href="/A332231/b332231.txt">Table of n, a(n) for n = 0..310</a>
%F A332231 a(n) = Sum_{k=0..n} binomial((n+1)*n,k) * binomial(n^2-k-1,n-k).
%F A332231 From _Vaclav Kotesovec_, Feb 08 2020: (Start)
%F A332231 a(n) ~ 2^(n - 1/2) * exp(n) * n^(n - 1/2) / sqrt(Pi).
%F A332231 a(n) = binomial(n*(n+1), 2*n) * binomial(2*n, n) / binomial(n*(n+1)/2, n). (End)
%t A332231 Table[Sum[Binomial[(n + 1)*n, k]*Binomial[n^2 - k - 1, n - k], {k, 0, n}], {n, 0, 15}] (* _Vaclav Kotesovec_, Feb 08 2020 *)
%t A332231 Table[Binomial[n*(n+1), 2*n] * Binomial[2*n, n] / Binomial[n*(n+1)/2, n], {n, 0, 15}] (* _Vaclav Kotesovec_, Feb 08 2020 *)
%o A332231 (PARI) {a(n) = sum(k=0, n, binomial((n+1)*n, k)*binomial(n^2-k-1,n-k))}
%Y A332231 Main diagonal of A330843.
%K A332231 nonn
%O A332231 0,2
%A A332231 _Seiichi Manyama_, Feb 08 2020