A222159 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 nondecreasing order

1, 2, 1, 6, 3, 1, 24, 21, 4, 1, 120, 277, 56, 5, 1, 720, 6322, 2132, 126, 6, 1, 5040, 215659, 207262, 12521, 252, 7, 1, 40320, 10218797, 38778082, 4907711, 60344, 462, 8, 1, 362880, 636984802

Offset

1,2

Comments

Table starts

.1.2...6....24.....120......720.....5040.....40320.362880

.1.3..21...277....6322...215659.10218797.636984802

.1.4..56..2132..207262.38778082

.1.5.126.12521.4907711

.1.6.252.60344

.1.7.462

.1.8

.1

Links

Table of n, a(n) for n=1..38.

Formula

Empirical for column k:

k=1: a(n) = 1

k=2: a(n) = n + 1

k=3: a(n) = (1/120)*n^5 + (1/8)*n^4 + (17/24)*n^3 + (15/8)*n^2 + (137/60)*n + 1

k=4: a(n) = [polynomial degree 18]

k=5: a(n) = [polynomial degree 79]

Example

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

Crossrefs

Column 3 is A000389(n+5)

Sequence in context: A221915 A249619 A345462 * A221623 A096334 A107867

Adjacent sequences: A222156 A222157 A222158 * A222160 A222161 A222162

Keyword

nonn,tabl

Author

R. H. Hardin Feb 10 2013

Status

approved