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 A349510 #6 Dec 05 2021 10:41:25 %S A349510 0,1,2,10395,709721037200,11641222531417506431654250, %T A349510 94310884171276301089942905465465961965897600, %U A349510 1948497841630989653689709780233830548909045113177792777217829860522656,192558458967017735390472923791964989275151544601992192306693834632003663346431678074519409150869009600 %N A349510 a(n) = binomial(n^3-floor(((n-1)^3+1)/2), 3*n^2-3*n+1) + binomial(n^3-floor(((n-1)^3+2)/2), 3*n^2-3*n+1). %C A349510 a(n) is a sharp upper bound of the number of vertices of the polytope of the n X n X n stochastic tensors, 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 Li et al. and Zhang et al.). %H A349510 Zhongshan Li, Fuzhen Zhang and Xiao-Dong Zhang, <a href="https://doi.org/10.1080/03081087.2017.1310178">On the number of vertices of the stochastic tensor polytope</a>, Linear and Multilinear Algebra, 65:10, 2064-2075, (2017). <a href="https://arxiv.org/abs/1702.04288">arXiv:1702.04288 [math.CO]</a>, 2017. See p. 4. %H A349510 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. 4. %F A349510 A349508(n)/A349509(n) <= a(n) < A349511(n) < A349512(n) (see Corollary 7 in Zhang et al., 2021). %F A349510 a(n) ~ (n/6)^(3*n*(n-1))*exp(-6+13/n+3*n^2)/(3*sqrt(6*Pi)). %t A349510 a[n_]:=Binomial[n^3-Floor[((n-1)^3+1)/2],3n^2-3n+1]+Binomial[n^3-Floor[((n-1)^3+2)/2],3n^2-3n+1]; Array[a,9,0] %Y A349510 Cf. A242658. %Y A349510 Cf. A349506, A349507, A349508, A349509, A349511, A349512. %K A349510 nonn %O A349510 0,3 %A A349510 _Stefano Spezia_, Nov 20 2021