A264635 - OEIS

%I #28 Sep 15 2022 08:07:05

%S 1,1,1,1,2,4,8,16,48,144,432,1296,5184,20736,82944,331776,1658880,

%T 8294400,41472000,207360000,1244160000,7464960000,44789760000,

%U 268738560000,1881169920000,13168189440000,92177326080000,645241282560000,5161930260480000

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

%H R. H. Hardin, <a href="/A264635/b264635.txt">Table of n, a(n) for n = 1..62</a>

%F a(n) = Product_{i=0..3} floor((n+i)/4)!. - _Alois P. Heinz_, Jul 12 2016

%F a(n) ~ Pi^(3/2) * n^(3/2) * n! / 2^(2*n + 5/2). - _Vaclav Kotesovec_, Oct 02 2018

%F Sum_{n>0} floor((n-1)/4)/a(n) = 1. - _Peter McNair_, May 29 2022

%e All solutions for n=6:

%e   0    4    4    0

%e   4    0    0    4

%e   1    1    5    5

%e   5    5    1    1

%e   2    2    2    2

%e   3    3    3    3

%t Table[Product[Floor[(n + i)/4]!, {i, 0, 3}], {n, 1, 30}] (* _Vaclav Kotesovec_, Oct 02 2018 *)

%Y Column 1 of A264638.

%Y Column k=4 of A275062.

%K nonn

%O 1,5

%A _R. H. Hardin_, Nov 19 2015