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A264791 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 7. 6
1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 384, 1152, 3456, 10368, 31104, 93312, 279936, 1119744, 4478976, 17915904, 71663616, 286654464, 1146617856, 4586471424, 22932357120, 114661785600, 573308928000, 2866544640000, 14332723200000, 71663616000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Column 1 of A264794.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..91

FORMULA

a(n) = Product_{i=0..6} floor((n+i)/7)!. - Alois P. Heinz, Jul 12 2016

a(n) ~ (2*Pi*n)^3 * n! / 7^(n + 7/2). - Vaclav Kotesovec, Oct 02 2018

EXAMPLE

All solutions for n=11

..0....0....7....0....7....0....7....7....7....7....0....0....0....7....0....7

..7....7....0....7....0....7....0....0....0....0....7....7....7....0....7....0

..1....1....8....8....8....1....1....8....1....8....8....8....8....1....1....1

..8....8....1....1....1....8....8....1....8....1....1....1....1....8....8....8

..9....2....2....9....9....2....9....2....2....9....9....2....2....9....9....2

..2....9....9....2....2....9....2....9....9....2....2....9....9....2....2....9

..3....3...10....3....3...10...10....3...10...10...10...10....3....3...10....3

.10...10....3...10...10....3....3...10....3....3....3....3...10...10....3...10

..4....4....4....4....4....4....4....4....4....4....4....4....4....4....4....4

..5....5....5....5....5....5....5....5....5....5....5....5....5....5....5....5

..6....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6

MATHEMATICA

Table[Product[Floor[(n + i)/7]!, {i, 0, 6}], {n, 1, 40}] (* Vaclav Kotesovec, Oct 02 2018 *)

CROSSREFS

Cf. A264794.

Column k=7 of A275062.

Sequence in context: A275074 A290687 A290855 * A290851 A290670 A079838

Adjacent sequences:  A264788 A264789 A264790 * A264792 A264793 A264794

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 25 2015

STATUS

approved

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Last modified December 9 03:42 EST 2021. Contains 349625 sequences. (Running on oeis4.)