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%I #3 Feb 10 2013 08:45:49
%S 1,2,1,6,3,1,24,21,4,1,120,277,56,5,1,720,6322,2132,126,6,1,5040,
%T 215659,207262,12521,252,7,1,40320,10218797,38778082,4907711,60344,
%U 462,8,1,362880,636984802
%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 nondecreasing order
%C Table starts
%C .1.2...6....24.....120......720.....5040.....40320.362880
%C .1.3..21...277....6322...215659.10218797.636984802
%C .1.4..56..2132..207262.38778082
%C .1.5.126.12521.4907711
%C .1.6.252.60344
%C .1.7.462
%C .1.8
%C .1
%F Empirical for column k:
%F k=1: a(n) = 1
%F k=2: a(n) = n + 1
%F k=3: a(n) = (1/120)*n^5 + (1/8)*n^4 + (17/24)*n^3 + (15/8)*n^2 + (137/60)*n + 1
%F k=4: a(n) = [polynomial degree 18]
%F k=5: a(n) = [polynomial degree 79]
%e Some solutions for n=3 k=4
%e ..2..4..1..3....1..4..2..3....1..2..4..3....1..4..2..3....2..1..3..4
%e ..3..1..2..4....2..4..1..3....1..3..2..4....2..1..3..4....3..4..1..2
%e ..3..4..1..2....4..1..3..2....3..1..2..4....3..4..2..1....3..4..1..2
%Y Column 3 is A000389(n+5)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Feb 10 2013
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