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

%S 1,1,2,1,6,6,1,14,74,24,1,34,852,1880,120,1,78,10210,152922,80316,720,

%T 1,178,124466,13745475,62038644,5141864,5040,1,398,1539739,1301306034,

%U 55575194220,47286888510,458608016,40320,1,882,19271229,128342085219

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 avoiding the pattern equal-up in every row and column.

%C Table starts

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

%C .....2.........6..........14..........34.............78..........178......398

%C .....6........74.........852.......10210.........124466......1539739.19271229

%C ....24......1880......152922....13745475.....1301306034.128342085219

%C ...120.....80316....62038644.55575194220.54180777470296

%C ...720...5141864.47286888510

%C ..5040.458608016

%C .40320

%H R. H. Hardin, <a href="/A269336/b269336.txt">Table of n, a(n) for n = 1..41</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000142.

%Y Row 2 is A059570(n+1).

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Feb 24 2016