A264656 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 5.

1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 96, 288, 864, 2592, 7776, 31104, 124416, 497664, 1990656, 7962624, 39813120, 199065600, 995328000, 4976640000, 24883200000, 149299200000, 895795200000, 5374771200000, 32248627200000, 193491763200000, 1354442342400000

Offset

1,6

Comments

Column 1 of A264659.

Links

R. H. Hardin, Table of n, a(n) for n = 1..74

Formula

a(n) = Product_{i=0..4} floor((n+i)/5)!. - Alois P. Heinz, Jul 12 2016

a(n) ~ (2*Pi*n)^2 * n! / 5^(n + 5/2). - Vaclav Kotesovec, Oct 02 2018

Example

All solutions for n=8
..5....0....0....5....5....5....0....0
..0....5....5....0....0....0....5....5
..1....6....6....6....6....1....1....1
..6....1....1....1....1....6....6....6
..7....7....2....2....7....2....7....2
..2....2....7....7....2....7....2....7
..3....3....3....3....3....3....3....3
..4....4....4....4....4....4....4....4

Mathematica

Table[Product[Floor[(n + i)/5]!, {i, 0, 4}], {n, 1, 30}] (* Vaclav Kotesovec, Oct 02 2018 *)

Crossrefs

Cf. A264659.

Column k=5 of A275062.

Sequence in context: A035523 A290301 A195458 * A078227 A250073 A260873

Adjacent sequences: A264653 A264654 A264655 * A264657 A264658 A264659

Keyword

nonn

Author

R. H. Hardin, Nov 20 2015

Status

approved