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A264557 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 3.

%I A264557 #13 Oct 02 2018 04:33:48
%S A264557 1,1,1,2,4,8,24,72,216,864,3456,13824,69120,345600,1728000,10368000,
%T A264557 62208000,373248000,2612736000,18289152000,128024064000,1024192512000,
%U A264557 8193540096000,65548320768000,589934886912000,5309413982208000,47784725839872000
%N A264557 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 3.
%C A264557 Column 1 of A264560.
%H A264557 R. H. Hardin, <a href="/A264557/b264557.txt">Table of n, a(n) for n = 1..48</a>
%F A264557 a(n) = Product_{i=0..2} ceiling((n-i)/3)!. - _Alois P. Heinz_, Jul 09 2016
%F A264557 a(n) ~ 2 * Pi * (n+1)! / 3^(n + 3/2). - _Vaclav Kotesovec_, Oct 02 2018
%e A264557 All solutions for n=4
%e A264557 ..0....3
%e A264557 ..3....0
%e A264557 ..1....1
%e A264557 ..2....2
%t A264557 Table[Product[Floor[(n + i)/3]!, {i, 0, 2}], {n, 1, 30}] (* _Vaclav Kotesovec_, Oct 02 2018 *)
%Y A264557 Cf. A264560.
%Y A264557 Column k=3 of A275062.
%K A264557 nonn
%O A264557 1,4
%A A264557 _R. H. Hardin_, Nov 17 2015