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A172544
Number of n X n 0..1 arrays with row sums 6 and column sums 6
3
0, 0, 0, 0, 0, 1, 5040, 187530840, 12025780892160, 1289144584143523800, 226885231700215713535680, 64051375889927380035549804336, 28278447454165011203551734584421120
OFFSET
1,7
COMMENTS
Also number of ways to arrange 6n rooks on an n X n chessboard, with no more than 6 rooks in each row and column. - Vaclav Kotesovec, Aug 04 2013
Generally (Canfield + McKay, 2004), a(n) ~ exp(-1/2)*binomial(n,s)^(2*n) / binomial(n^2,s*n), or a(n) ~ sqrt(2*Pi)*exp(-n*s-1/2*(s-1)^2)*(n*s)^(n*s+1/2)*(s!)^(-2*n). - Vaclav Kotesovec, Aug 04 2013
FORMULA
From Vaclav Kotesovec, Aug 04 2013: (Start)
a(n) ~ exp(-1/2)*binomial(n,6)^(2*n)/binomial(n^2,6*n), (Canfield + McKay, 2004)
a(n) ~ sqrt(Pi)*2^(1-2*n)*3^(2*n+1/2)*5^(-2*n)*exp(-6*n-25/2)*n^(6*n+1/2)
(End)
CROSSREFS
Column 6 of A008300.
Sequence in context: A318714 A227669 A010800 * A287083 A158039 A071549
KEYWORD
nonn
AUTHOR
R. H. Hardin Feb 06 2010
STATUS
approved