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T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with column sums equal.
5

%I #6 Aug 12 2016 06:55:35

%S 1,1,2,1,4,6,1,8,36,24,1,16,216,648,120,1,32,1296,19584,19800,720,1,

%T 64,7776,643680,4140000,972000,5040,1,128,46656,22374144,1007460000,

%U 1936704000,69060600,40320,1,256,279936,807480576,269568000000

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with column sums equal.

%C Table starts

%C ......1..........1.............1.............1............1..............1

%C ......2..........4.............8............16...........32.............64

%C ......6.........36...........216..........1296.........7776..........46656

%C .....24........648.........19584........643680.....22374144......807480576

%C ....120......19800.......4140000....1007460000.269568000000.76711698000000

%C ....720.....972000....1936704000.4757348160000

%C ...5040...69060600.1610574336000

%C ..40320.6756825600

%C .362880

%H R. H. Hardin, <a href="/A268472/b268472.txt">Table of n, a(n) for n = 1..50</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Diagonal is A268362.

%Y Column 1 is A000142.

%Y Row 2 is A000079.

%Y Row 3 is A000400.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Feb 05 2016