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A222005
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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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6
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1, 2, 1, 6, 2, 1, 24, 12, 2, 1, 120, 157, 22, 2, 1, 720, 3853, 704, 37, 2, 1, 5040, 138715, 78376, 2470, 58, 2, 1, 40320, 6838453, 15637284, 1227685, 7328, 86, 2, 1, 362880, 438350738, 5360397488, 1252017597, 16011558, 19228, 122, 2, 1, 3628800
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OFFSET
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1,2
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COMMENTS
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Table starts
.1.2...6....24......120........720.......5040.........40320......362880.3628800
.1.2..12...157.....3853.....138715....6838453.....438350738.35526122154
.1.2..22...704....78376...15637284.5360397488.2687794004996
.1.2..37..2470..1227685.1252017597
.1.2..58..7328.16011558
.1.2..86.19228
.1.2.122
.1.2
.1
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LINKS
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EXAMPLE
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Some solutions for n=3 k=4
..4..1..3..2....2..4..1..3....4..1..3..2....3..4..1..2....3..2..4..1
..2..1..4..3....1..4..2..3....3..4..2..1....3..1..4..2....3..1..4..2
..2..1..4..3....1..4..2..3....3..2..4..1....1..4..3..2....2..4..3..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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