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A212930
T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than column j-1 in all rows
14
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
OFFSET
1,2
COMMENTS
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
LINKS
FORMULA
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)
EXAMPLE
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
CROSSREFS
Column 2 is A024036
Row 1 is A001700(n-1)
Sequence in context: A176740 A370258 A134991 * A225725 A095327 A225753
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin May 31 2012
STATUS
approved