A212930 T(n,k) = number of n X k 0..k-1 arrays with no column j greater than column j-1 in all rows.

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

Author

R. H. Hardin, May 31 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..172

Crossrefs

Column 2 is A024036.

Row 1 is A001700(n-1).

Cf. A212943.

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) [phone]*a(n-5)

The coefficient of a(n-1) is A209671(k) (through at least k=1..7)