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T(n,k)=Number of nXk arrays with each row a permutation of 1..k having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order
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%I #4 Feb 03 2013 09:29:48

%S 1,2,1,6,2,1,24,12,2,1,120,157,22,2,1,720,3853,704,37,2,1,5040,138715,

%T 78376,2470,58,2,1,40320,6838453,15637284,1227685,7328,86,2,1,362880,

%U 438350738,5360397488,1252017597,16011558,19228,122,2,1,3628800

%N T(n,k)=Number of nXk arrays with each row a permutation of 1..k having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order

%C Table starts

%C .1.2...6....24......120........720.......5040.........40320......362880.3628800

%C .1.2..12...157.....3853.....138715....6838453.....438350738.35526122154

%C .1.2..22...704....78376...15637284.5360397488.2687794004996

%C .1.2..37..2470..1227685.1252017597

%C .1.2..58..7328.16011558

%C .1.2..86.19228

%C .1.2.122

%C .1.2

%C .1

%H R. H. Hardin, <a href="/A222005/b222005.txt">Table of n, a(n) for n = 1..48</a>

%e Some solutions for n=3 k=4

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

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

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Feb 03 2013