

A088021


a(n) = (n^2)!/(n!)^2.


9




OFFSET

0,3


COMMENTS

Based on an observation of Hugo Pfoertner, W. Edwin Clark, conjectured and Xiangdong 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.
Using J. T. Schwarz' 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.
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.


LINKS



FORMULA



PROG

(Magma) [Factorial(n^2)/Factorial(n)^2: n in [0..10]]; // Vincenzo Librandi, May 31 2011


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



