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 A088021 #14 Oct 14 2023 23:33:08 %S A088021 1,1,6,10080,36324288000,1077167364120207360000, %T A088021 717579719887926731226850787328000000, %U A088021 23946596436219275985459662514223331478629410406400000000 %N A088021 a(n) = (n^2)!/(n!)^2. %C A088021 Based on an observation of _Hugo Pfoertner_, _W. Edwin Clark_ conjectured and Xiang-dong Hou proved that (n^2)!/(n!)^2 gives the number of distinct determinants of the generic n X n matrix whose entries are n^2 different indeterminates under all (n^2)! permutations of the entries. %C A088021 Using J. T. Schwarz's Sparse Zeros Lemma this implies that for any positive integer n there is an n X n matrix A with positive integer entries such that the set of determinant values obtained from A by permuting the elements of A is (n^2)!/(n!)^2. %C A088021 Moreover, for any entries, no larger number of determinants can be obtained. In fact, by the Sparse Zeros Lemma one can select the entries of A from any sufficiently large subset of real numbers. %H A088021 Vincenzo Librandi, <a href="/A088021/b088021.txt">Table of n, a(n) for n = 0..21</a> %F A088021 a(n) = A088020(n)/A001044(n). %o A088021 (Magma) [Factorial(n^2)/Factorial(n)^2: n in [0..10]]; // _Vincenzo Librandi_, May 31 2011 %Y A088021 Cf. A001044, A088020. %K A088021 nonn %O A088021 0,3 %A A088021 _Hugo Pfoertner_, Sep 18 2003