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 A350595 #16 Jan 15 2022 02:54:28
%S A350595 1,0,6,1680,5562130,248832363780,157933807781230404,
%T A350595 1459371378373349655614400,199540356506880704345957381087490,
%U A350595 408278793226256174470138460253382778465100,12605249484391847030759523774663513363531264829120276
%N A350595 a(n) = Sum_{k=0..2*n} (-1)^(n+k) * binomial(2*n,k)^n.
%F A350595 a(n) ~ c * A224733 = c * binomial(2*n, n)^n, where c = 0.30062580086898437298921168710510240913792796183034926496082316066508397... - _Vaclav Kotesovec_, Jan 15 2022
%t A350595 Table[Sum[(-1)^(n+k)*Binomial[2*n,k]^n,{k,0,2n}],{n,0,10}] (* _Stefano Spezia_, Jan 08 2022 *)
%o A350595 (PARI) a(n) = sum(k=0, 2*n, (-1)^(n+k)*binomial(2*n, k)^n);
%o A350595 (Python)
%o A350595 from math import comb
%o A350595 def A350595(n): return sum((-1 if (n+k) % 2 else 1)*comb(2*n,k)**n for k in range(2*n+1)) # _Chai Wah Wu_, Jan 08 2022
%Y A350595 Main diagonal of A350594.
%Y A350595 Cf. A224733.
%K A350595 nonn
%O A350595 0,3
%A A350595 _Seiichi Manyama_, Jan 08 2022