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

1,5

Links

Table of n, a(n) for n=1..39.

Example

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.

Sequence in context: A177262 A203092 A139167 * A323849 A254442 A340476

Adjacent sequences: A211706 A211707 A211708 * A211710 A211711 A211712

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 19 2012

Status

approved