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A215293 Number of permutations of 0..floor((n*n-2)/2) on odd squares of an n X n array such that each row and column of odd squares is increasing.

%I A215293 #14 Sep 02 2025 11:46:38
%S A215293 1,2,6,280,23100,85765680,577185873264,346915095471584640,
%T A215293 381134230556959188429120,62144711688730139887005809020800,
%U A215293 18592619468814454675301397184588597886400,1236552808693429892089668394551052130596983991526400,151213938214745201135492692441902799026853717717324113365952000
%N A215293 Number of permutations of 0..floor((n*n-2)/2) on odd squares of an n X n array such that each row and column of odd squares is increasing.
%H A215293 R. H. Hardin, <a href="/A215293/b215293.txt">Table of n, a(n) for n = 1..40</a>
%F A215293 T(n,k) = A060854(f1,f2)*A060854(f2,f1)*binomial(f1*f2+f2*f1,f1*f2) with f1 = floor(n/2) and f2 = floor((n+1)/2).
%e A215293 Some solutions for n=5
%e A215293 ..x..0..x..4..x....x..4..x..6..x....x..1..x..6..x....x..0..x..6..x
%e A215293 ..1..x..3..x..7....0..x..1..x..9....0..x..2..x..3....3..x..4..x..9
%e A215293 ..x..2..x..5..x....x..5..x..8..x....x..7..x..8..x....x..1..x..7..x
%e A215293 ..8..x..9..x.10....2..x..3..x.10....4..x..5..x.11....5..x..8..x.11
%e A215293 ..x..6..x.11..x....x..7..x.11..x....x..9..x.10..x....x..2..x.10..x
%Y A215293 Diagonal of A215297.
%Y A215293 Cf. A060854.
%K A215293 nonn,changed
%O A215293 1,2
%A A215293 _R. H. Hardin_, Aug 07 2012