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.

1, 2, 6, 280, 23100, 85765680, 577185873264, 346915095471584640, 381134230556959188429120, 62144711688730139887005809020800, 18592619468814454675301397184588597886400, 1236552808693429892089668394551052130596983991526400, 151213938214745201135492692441902799026853717717324113365952000

Offset: 1

Author

R. H. Hardin, Aug 07 2012

Keywords

• nonn
• changed

Examples

			Some solutions for n=5
..x..0..x..4..x....x..4..x..6..x....x..1..x..6..x....x..0..x..6..x
..1..x..3..x..7....0..x..1..x..9....0..x..2..x..3....3..x..4..x..9
..x..2..x..5..x....x..5..x..8..x....x..7..x..8..x....x..1..x..7..x
..8..x..9..x.10....2..x..3..x.10....4..x..5..x.11....5..x..8..x.11
..x..6..x.11..x....x..7..x.11..x....x..9..x.10..x....x..2..x.10..x
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..40

Crossrefs

Diagonal of A215297.

Cf. A060854.

Formula

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).