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A212930
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T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than column j-1 in all rows
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14
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1, 3, 1, 10, 15, 1, 35, 568, 63, 1, 126, 39695, 18226, 255, 1, 462, 4431876, 14177855, 518320, 1023, 1, 1716, 724082352, 23124921876, 4041974015, 14230810, 4095, 1, 6435, 163050236504, 68264066143602, 85800824609376, 1075113010175, 386357608
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OFFSET
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1,2
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COMMENTS
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Table starts
.1....3.......10............35................126......................462
.1...15......568.........39695............4431876................724082352
.1...63....18226......14177855........23124921876...........68264066143602
.1..255...518320....4041974015.....85800824609376......4051316109991426752
.1.1023.14230810.1075113010175.285912852294921876.207406617181155352354002
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 5*a(n-1) -4*a(n-2)
k=3: a(n) = 37*a(n-1) -279*a(n-2) +243*a(n-3)
k=4: a(n) = 405*a(n-1) -43860*a(n-2) +1524160*a(n-3) -15636480*a(n-4) +14155776*a(n-5)
The coefficient of a(n-1) is A209671(k) (through at least k=1..7)
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EXAMPLE
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Some solutions for n=3 k=4
..2..0..1..0....1..0..0..0....3..1..1..1....1..0..2..3....2..2..1..0
..2..0..1..2....0..3..1..2....3..2..3..0....2..1..1..0....0..3..0..0
..1..3..0..0....1..0..1..3....1..1..1..1....3..3..0..1....1..1..1..3
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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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