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 A264656 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 5. 7

%I #19 Sep 15 2022 08:06:53

%S 1,1,1,1,1,2,4,8,16,32,96,288,864,2592,7776,31104,124416,497664,

%T 1990656,7962624,39813120,199065600,995328000,4976640000,24883200000,

%U 149299200000,895795200000,5374771200000,32248627200000,193491763200000,1354442342400000

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

%C Column 1 of A264659.

%H R. H. Hardin, <a href="/A264656/b264656.txt">Table of n, a(n) for n = 1..74</a>

%F a(n) = Product_{i=0..4} floor((n+i)/5)!. - _Alois P. Heinz_, Jul 12 2016

%F a(n) ~ (2*Pi*n)^2 * n! / 5^(n + 5/2). - _Vaclav Kotesovec_, Oct 02 2018

%e All solutions for n=8

%e ..5....0....0....5....5....5....0....0

%e ..0....5....5....0....0....0....5....5

%e ..1....6....6....6....6....1....1....1

%e ..6....1....1....1....1....6....6....6

%e ..7....7....2....2....7....2....7....2

%e ..2....2....7....7....2....7....2....7

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

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

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

%Y Cf. A264659.

%Y Column k=5 of A275062.

%K nonn

%O 1,6

%A _R. H. Hardin_, Nov 20 2015

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Last modified October 4 23:44 EDT 2023. Contains 365888 sequences. (Running on oeis4.)