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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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

R. H. Hardin, Table of n, a(n) for n=1..28

E. R. Canfield and B. D. McKay, Asymptotic enumeration of dense 0-1 matrices with equal row and column sums, Electron. J. Combin. 12 (2005)

Shalosh B. Ekhad and Doron Zeilberger, In How Many Ways Can n (Straight) Men and n (Straight) Women Get Married, if Each Person Has Exactly k Spouses

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: A221622 A227669 A010800 * A287083 A158039 A071549

Adjacent sequences:  A172541 A172542 A172543 * A172545 A172546 A172547

KEYWORD

nonn

AUTHOR

R. H. Hardin Feb 06 2010

STATUS

approved

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Last modified May 23 12:45 EDT 2017. Contains 286915 sequences.