A222005 T(n,k)=Number of nXk arrays with each row a permutation of 1..k having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order

1, 2, 1, 6, 2, 1, 24, 12, 2, 1, 120, 157, 22, 2, 1, 720, 3853, 704, 37, 2, 1, 5040, 138715, 78376, 2470, 58, 2, 1, 40320, 6838453, 15637284, 1227685, 7328, 86, 2, 1, 362880, 438350738, 5360397488, 1252017597, 16011558, 19228, 122, 2, 1, 3628800

Offset

1,2

Comments

Table starts

.1.2...6....24......120........720.......5040.........40320......362880.3628800

.1.2..12...157.....3853.....138715....6838453.....438350738.35526122154

.1.2..22...704....78376...15637284.5360397488.2687794004996

.1.2..37..2470..1227685.1252017597

.1.2..58..7328.16011558

.1.2..86.19228

.1.2.122

.1.2

.1

Links

R. H. Hardin, Table of n, a(n) for n = 1..48

Example

Some solutions for n=3 k=4
..4..1..3..2....2..4..1..3....4..1..3..2....3..4..1..2....3..2..4..1
..2..1..4..3....1..4..2..3....3..4..2..1....3..1..4..2....3..1..4..2
..2..1..4..3....1..4..2..3....3..2..4..1....1..4..3..2....2..4..3..1

Crossrefs

Sequence in context: A157392 A321352 A134134 * A351442 A325815 A292441

Adjacent sequences: A222002 A222003 A222004 * A222006 A222007 A222008

Keyword

nonn,tabl

Author

R. H. Hardin Feb 03 2013

Status

approved