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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. 1
1, 2, 6, 280, 23100, 85765680, 577185873264, 346915095471584640, 381134230556959188429120, 62144711688730139887005809020800, 18592619468814454675301397184588597886400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

f1=floor(n/2),

f2=floor((n+1)/2),

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

EXAMPLE

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

CROSSREFS

Diagonal of A215297.

Sequence in context: A007190 A164829 A028337 * A264410 A135014 A321571

Adjacent sequences:  A215290 A215291 A215292 * A215294 A215295 A215296

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 07 2012

STATUS

approved

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Last modified January 24 21:49 EST 2022. Contains 350565 sequences. (Running on oeis4.)