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%I #23 Jan 20 2021 20:50:32
%S 1,1,1,1,1,1,2,4,8,16,32,64,192,576,1728,5184,15552,46656,186624,
%T 746496,2985984,11943936,47775744,191102976,955514880,4777574400,
%U 23887872000,119439360000,597196800000,2985984000000,17915904000000,107495424000000,644972544000000
%N Number of n X 1 arrays of permutations of 0..n-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 6.
%C Column 1 of A264704.
%H R. H. Hardin, <a href="/A264701/b264701.txt">Table of n, a(n) for n = 1..84</a>
%F a(n) = Product_{i=0..5} floor((n+i)/6)!. - _Alois P. Heinz_, Jul 12 2016
%F a(n) ~ (2*Pi*n)^(5/2) * n! / 6^(n + 3). - _Vaclav Kotesovec_, Oct 02 2018
%e All solutions for n=8
%e ..6....6....0....0
%e ..0....0....6....6
%e ..7....1....1....7
%e ..1....7....7....1
%e ..2....2....2....2
%e ..3....3....3....3
%e ..4....4....4....4
%e ..5....5....5....5
%t Table[Product[Floor[(n + i)/6]!, {i, 0, 5}], {n, 1, 40}] (* _Vaclav Kotesovec_, Oct 02 2018 *)
%Y Cf. A264704.
%Y Column k=6 of A275062.
%K nonn
%O 1,7
%A _R. H. Hardin_, Nov 21 2015
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