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%I #11 Jan 16 2024 18:29:18
%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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