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.

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

Author

R. H. Hardin May 31 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..191

Crossrefs

Column 2 is A005061

cf. A212930

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) [phone]*a(n-3) -702208000*a(n-4) [phone]*a(n-5)

The coefficient of a(n-1) is A209668(k) (through at least k=1..7)