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T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column greater than the previous repeated value.
5

%I #4 Jan 28 2016 16:03:56

%S 2,9,4,60,81,6,570,3600,576,9,6960,324900,178068,3969,12,104006,

%T 48441600,157322070,8459154,25281,16,1837752,10817248036,292870561470,

%U 73055876226,376812420,155236,20,37478718,3377332413504,994136348047368

%N T(n,k)=Number of nXk 0..k arrays with every repeated value in every row and column greater than the previous repeated value.

%C Table starts

%C ..2......9..........60............570.............6960...............104006

%C ..4.....81........3600.........324900.........48441600..........10817248036

%C ..6....576......178068......157322070.....292870561470......994136348047368

%C ..9...3969.....8459154....73055876226.1699631089239529.87855957137937824257

%C .12..25281...376812420.32082001964881

%C .16.155236.16109362560

%C .20.915849

%C .25

%H R. H. Hardin, <a href="/A268204/b268204.txt">Table of n, a(n) for n = 1..40</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A002620(n+2).

%Y Column 2 is A267961.

%Y Column 3 is A267930.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 28 2016