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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

%I

%S 1,1,1,1,1,1,1,2,4,8,16,32,64,128,384,1152,3456,10368,31104,93312,

%T 279936,1119744,4478976,17915904,71663616,286654464,1146617856,

%U 4586471424,22932357120,114661785600,573308928000,2866544640000,14332723200000,71663616000000

%N Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 7.

%C Column 1 of A264794.

%H R. H. Hardin, <a href="/A264791/b264791.txt">Table of n, a(n) for n = 1..91</a>

%F a(n) = Product_{i=0..6} floor((n+i)/7)!. - _Alois P. Heinz_, Jul 12 2016

%F a(n) ~ (2*Pi*n)^3 * n! / 7^(n + 7/2). - _Vaclav Kotesovec_, Oct 02 2018

%e All solutions for n=11

%e ..0....0....7....0....7....0....7....7....7....7....0....0....0....7....0....7

%e ..7....7....0....7....0....7....0....0....0....0....7....7....7....0....7....0

%e ..1....1....8....8....8....1....1....8....1....8....8....8....8....1....1....1

%e ..8....8....1....1....1....8....8....1....8....1....1....1....1....8....8....8

%e ..9....2....2....9....9....2....9....2....2....9....9....2....2....9....9....2

%e ..2....9....9....2....2....9....2....9....9....2....2....9....9....2....2....9

%e ..3....3...10....3....3...10...10....3...10...10...10...10....3....3...10....3

%e .10...10....3...10...10....3....3...10....3....3....3....3...10...10....3...10

%e ..4....4....4....4....4....4....4....4....4....4....4....4....4....4....4....4

%e ..5....5....5....5....5....5....5....5....5....5....5....5....5....5....5....5

%e ..6....6....6....6....6....6....6....6....6....6....6....6....6....6....6....6

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

%Y Cf. A264794.

%Y Column k=7 of A275062.

%K nonn

%O 1,8

%A _R. H. Hardin_, Nov 25 2015

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Last modified January 25 10:12 EST 2022. Contains 350565 sequences. (Running on oeis4.)