OFFSET
1,3
COMMENTS
The row for n begins with n-1 zeros since a matrix with fewer than n ones has an all-zero row.
The last entry in the row for n is T(n, n^2-n+1) as a matrix with more than n^2-n+1 ones must have two identical rows.
Each entry in the row for n is a multiple of n! since rows must be distinct.
LINKS
Mathoverflow, The number of non-singular n x n matrices over F2 with exactly k non-zero entries, posted 12 Jun 2019. Rows for n = 3 and n = 4 given by Richard Stanley in a comment.
FORMULA
T(n, n) = n!, T(n, n+1) = n!*n*(n-1), T(n, n^2-n+1) = n!*n (Weg, see Mathoverflow link).
EXAMPLE
T(2,3) = 4 from the 2 X 2 nonsingular matrices (1,1;1,0), (1,1;0,1), (1,0;1,1), and (0,1;1,1) which each have 3 ones.
Triangle begins
1
0 2 4
0 0 6 36 72 36 18
0 0 0 24 288 1440 3648 4752 4992 2592 1728 600 96
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Brian Hopkins, Jul 17 2019
STATUS
approved