A211709 T(n,k) = number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and every value unique in its row and column.

1, 1, 1, 1, 4, 1, 1, 18, 18, 1, 1, 108, 588, 108, 1, 1, 780, 30240, 30240, 780, 1, 1, 6600, 2277600, 17427192, 2277600, 6600, 1, 1, 63840, 234440280, 17741309400, 17741309400, 234440280, 63840, 1, 1, 693840, 31448589480

Offset: 1

Author

R. H. Hardin, Apr 19 2012

Keywords

• nonn
• tabl

Examples

			Table starts:
  1     1         1           1           1         1           1      1 1
  1     4        18         108         780      6600       63840 693840
  1    18       588       30240     2277600 234440280 31448589480
  1   108     30240    17427192 17741309400
  1   780   2277600 17741309400
  1  6600 234440280
  1 63840
  1
Some solutions for n=4, k=4:
  0 1 2 3    0 1 2 3    0 1 2 3    0 1 2 3    0 1 2 3
  1 4 0 2    1 2 0 4    4 2 0 1    1 0 3 2    1 0 3 2
  2 0 5 1    2 0 1 5    1 0 3 2    2 3 0 4    4 2 0 1
  3 2 1 4    3 4 5 0    2 3 1 0    3 2 1 0    5 3 1 0
		

Crossrefs

Column 2 is A144085.