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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

%I

%S 1,1,1,1,4,1,1,18,18,1,1,108,588,108,1,1,780,30240,30240,780,1,1,6600,

%T 2277600,17427192,2277600,6600,1,1,63840,234440280,17741309400,

%U 17741309400,234440280,63840,1,1,693840,31448589480

%N 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.

%e Table starts:

%e .1.....1.........1...........1...........1.........1...........1......1.1

%e .1.....4........18.........108.........780......6600.......63840.693840

%e .1....18.......588.......30240.....2277600.234440280.31448589480

%e .1...108.....30240....17427192.17741309400

%e .1...780...2277600.17741309400

%e .1..6600.234440280

%e .1.63840

%e .1

%e Some solutions for n=4, k=4:

%e ..0..1..2..3....0..1..2..3....0..1..2..3....0..1..2..3....0..1..2..3

%e ..1..4..0..2....1..2..0..4....4..2..0..1....1..0..3..2....1..0..3..2

%e ..2..0..5..1....2..0..1..5....1..0..3..2....2..3..0..4....4..2..0..1

%e ..3..2..1..4....3..4..5..0....2..3..1..0....3..2..1..0....5..3..1..0

%Y Column 2 is A144085.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Apr 19 2012

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Last modified June 1 01:58 EDT 2020. Contains 334758 sequences. (Running on oeis4.)