%I #9 Jan 20 2024 13:59:25

%S 1,2,10,280,60060,85765680,2061378118800,346915095471584640,

%T 1736278161426147413954880,62144711688730139887005809020800,

%U 103104526145243794108489566205445861006400

%N Number of permutations of 0..floor((n*n-1)/2) on even squares of an n X n array such that each row and column of even squares is increasing.

%C Diagonal of A215292.

%H R. H. Hardin, <a href="/A215286/b215286.txt">Table of n, a(n) for n = 1..40</a>

%F f1 = floor((n+1)/2)

%F f2 = floor(n/2)

%F T(n,k) = A060854(f1,f1)*A060854(f2,f2)*binomial(f1*f1+f2*f2,f1*f1).

%e Some solutions for n=5

%e ..0..x..1..x..2....0..x..2..x..6....0..x..2..x..4....1..x..2..x..6

%e ..x..4..x..7..x....x..1..x..3..x....x..3..x..5..x....x..0..x..8..x

%e ..3..x..6..x..9....5..x..8..x.11....1..x..8..x..9....3..x..5..x.10

%e ..x..5..x.11..x....x..4..x..9..x....x..7..x.10..x....x..9..x.12..x

%e ..8..x.10..x.12....7..x.10..x.12....6..x.11..x.12....4..x..7..x.11

%Y Cf. A060854, A215292.

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 07 2012