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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.
9
1, 1, 1, 1, 2, 4, 8, 16, 48, 144, 432, 1296, 5184, 20736, 82944, 331776, 1658880, 8294400, 41472000, 207360000, 1244160000, 7464960000, 44789760000, 268738560000, 1881169920000, 13168189440000, 92177326080000, 645241282560000, 5161930260480000
OFFSET
1,5
LINKS
FORMULA
a(n) = Product_{i=0..3} floor((n+i)/4)!. - Alois P. Heinz, Jul 12 2016
a(n) ~ Pi^(3/2) * n^(3/2) * n! / 2^(2*n + 5/2). - Vaclav Kotesovec, Oct 02 2018
Sum_{n>0} floor((n-1)/4)/a(n) = 1. - Peter McNair, May 29 2022
EXAMPLE
All solutions for n=6:
0 4 4 0
4 0 0 4
1 1 5 5
5 5 1 1
2 2 2 2
3 3 3 3
MATHEMATICA
Table[Product[Floor[(n + i)/4]!, {i, 0, 3}], {n, 1, 30}] (* Vaclav Kotesovec, Oct 02 2018 *)
CROSSREFS
Column 1 of A264638.
Column k=4 of A275062.
Sequence in context: A096853 A027155 A129335 * A046237 A013084 A263535
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 19 2015
STATUS
approved