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 A349507 #21 Aug 31 2023 07:55:39
%S A349507 1,1,27,256,30517578125,531441,378818692265664781682717625943,
%T A349507 1208925819614629174706176,
%U A349507 8727963568087712425891397479476727340041449,867361737988403547205962240695953369140625,12527829399838427440107579247354215251149392000034969484678615956504532008683916069945559954314411495091
%N A349507 a(n) is the denominator of n!^(2*n)/(n^n^2).
%C A349507 a(n) is the denominator of a lower bound of the number of the vertices of the polytope of stochastic semi-magic n X n X n cubes, or equivalently, of the number of Latin squares of order n, or equivalently, of the number of n X n X n line-stochastic (0,1)-tensors (see Ahmed et al. and Zhang et al.).
%H A349507 Stefano Spezia, <a href="/A349507/b349507.txt">Table of n, a(n) for n = 1..28</a>
%H A349507 Maya Mohsin Ahmed, <a href="https://arxiv.org/abs/math/0405476">Algebraic Combinatorics of Magic Squares</a>, University of California - Davis, Ph.D. Thesis, 2004; arXiv:math/0405476 [math.CO], 2004. See p. 43.
%H A349507 Maya Mohsin Ahmed, Jesús De Loera and Raymond Hemmecke, <a href="https://doi.org/10.1007/978-3-642-55566-4_2">Polyhedral Cones of Magic Cubes and Squares</a>. In: Aronov B., Basu S., Pach J., Sharir M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg (2003). <a href="https://arxiv.org/abs/math/0201108">arXiv:math/0201108 [math.CO]</a>, 2002. See p. 3.
%H A349507 Fuzhen Zhang and Xiao-Dong Zhang, <a href="https://arxiv.org/abs/2110.12337">Comparison of the upper bounds for the extreme points of the polytopes of line-stochastic tensors</a>, arXiv:2110.12337 [math.CO], 2021. See p. 3.
%F A349507 A349506(n)/a(n) ~ n^(-n^2)*(exp(-n)*n^(n-1/2)*(1+12*n))^(2*n)*(Pi/72)^n.
%t A349507 Table[Denominator[n!^(2n)/(n^n^2)],{n,11}]
%o A349507 (PARI) a(n) = denominator(n!^(2*n)/n^n^2); \\ _Michel Marcus_, Nov 22 2021
%Y A349507 Cf. A000142, A000290, A002489, A005843, A185141.
%Y A349507 Cf. A349506 (numerators), A349508, A349509, A349510, A349511, A349512.
%K A349507 nonn,frac
%O A349507 1,3
%A A349507 _Stefano Spezia_, Nov 20 2021