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A212943
T(n,k)=Number of nXk 0..k-1 arrays with no column j greater than or equal to than column j-1 in all rows
14
1, 1, 1, 1, 7, 1, 1, 181, 37, 1, 1, 10311, 9019, 175, 1, 1, 1016501, 6470341, 331489, 781, 1, 1, 152747323, 10058484751, 2509306671, 10669771, 3367, 1, 1, 32383630189, 28744943858947, 52311221188001, 801439905901, 320396041, 14197, 1, 1
OFFSET
1,5
COMMENTS
Table starts
.1...1........1............1..................1........................1
.1...7......181........10311............1016501................152747323
.1..37.....9019......6470341........10058484751...........28744943858947
.1.175...331489...2509306671.....52311221188001......2438624218076957695
.1.781.10669771.801439905901.212180664326328751.153322267564381742818531
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 7*a(n-1) -12*a(n-2)
k=3: a(n) = 55*a(n-1) -936*a(n-2) +4860*a(n-3)
k=4: a(n) = 631*a(n-1) -144700*a(n-2) +15035200*a(n-3) -702208000*a(n-4) +11468800000*a(n-5)
The coefficient of a(n-1) is A209668(k) (through at least k=1..7)
EXAMPLE
Some solutions for n=4 k=4
..1..3..2..2....0..0..0..3....1..3..0..1....1..3..2..1....1..3..3..3
..1..1..2..2....0..1..1..2....0..0..1..0....1..1..0..3....2..3..0..3
..0..1..3..1....0..2..2..1....0..1..1..3....2..3..3..0....0..2..0..2
..3..1..0..3....2..1..0..2....3..0..3..1....1..0..3..0....2..0..1..0
CROSSREFS
Column 2 is A005061
Sequence in context: A188644 A331899 A111830 * A174588 A366316 A199001
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin May 31 2012
STATUS
approved