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A268472 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with column sums equal.

%I A268472 #6 Aug 12 2016 06:55:35
%S A268472 1,1,2,1,4,6,1,8,36,24,1,16,216,648,120,1,32,1296,19584,19800,720,1,
%T A268472 64,7776,643680,4140000,972000,5040,1,128,46656,22374144,1007460000,
%U A268472 1936704000,69060600,40320,1,256,279936,807480576,269568000000
%N A268472 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with column sums equal.
%C A268472 Table starts
%C A268472 ......1..........1.............1.............1............1..............1
%C A268472 ......2..........4.............8............16...........32.............64
%C A268472 ......6.........36...........216..........1296.........7776..........46656
%C A268472 .....24........648.........19584........643680.....22374144......807480576
%C A268472 ....120......19800.......4140000....1007460000.269568000000.76711698000000
%C A268472 ....720.....972000....1936704000.4757348160000
%C A268472 ...5040...69060600.1610574336000
%C A268472 ..40320.6756825600
%C A268472 .362880
%H A268472 R. H. Hardin, <a href="/A268472/b268472.txt">Table of n, a(n) for n = 1..50</a>
%e A268472 Some solutions for n=3 k=4
%e A268472 ..2..2..2..2. .1..2..0..1. .0..1..2..2. .0..1..1..2. .0..2..1..0
%e A268472 ..1..0..1..0. .0..0..2..2. .1..0..1..1. .1..2..2..1. .2..0..2..1
%e A268472 ..0..1..0..1. .2..1..1..0. .2..2..0..0. .2..0..0..0. .1..1..0..2
%Y A268472 Diagonal is A268362.
%Y A268472 Column 1 is A000142.
%Y A268472 Row 2 is A000079.
%Y A268472 Row 3 is A000400.
%K A268472 nonn,tabl
%O A268472 1,3
%A A268472 _R. H. Hardin_, Feb 05 2016