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A264635 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.

%I A264635 #28 Sep 15 2022 08:07:05
%S A264635 1,1,1,1,2,4,8,16,48,144,432,1296,5184,20736,82944,331776,1658880,
%T A264635 8294400,41472000,207360000,1244160000,7464960000,44789760000,
%U A264635 268738560000,1881169920000,13168189440000,92177326080000,645241282560000,5161930260480000
%N A264635 Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.
%H A264635 R. H. Hardin, <a href="/A264635/b264635.txt">Table of n, a(n) for n = 1..62</a>
%F A264635 a(n) = Product_{i=0..3} floor((n+i)/4)!. - _Alois P. Heinz_, Jul 12 2016
%F A264635 a(n) ~ Pi^(3/2) * n^(3/2) * n! / 2^(2*n + 5/2). - _Vaclav Kotesovec_, Oct 02 2018
%F A264635 Sum_{n>0} floor((n-1)/4)/a(n) = 1. - _Peter McNair_, May 29 2022
%e A264635 All solutions for n=6:
%e A264635   0    4    4    0
%e A264635   4    0    0    4
%e A264635   1    1    5    5
%e A264635   5    5    1    1
%e A264635   2    2    2    2
%e A264635   3    3    3    3
%t A264635 Table[Product[Floor[(n + i)/4]!, {i, 0, 3}], {n, 1, 30}] (* _Vaclav Kotesovec_, Oct 02 2018 *)
%Y A264635 Column 1 of A264638.
%Y A264635 Column k=4 of A275062.
%K A264635 nonn
%O A264635 1,5
%A A264635 _R. H. Hardin_, Nov 19 2015