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A075754
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Number of n X n (0,1) matrices containing exactly five 1's in each row and in each column.
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4
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1, 720, 3110940, 24046189440, 315031400802720, 6736218287430460752, 226885231700215713535680, 11649337108041078980732943360, 885282776210120715086715619724160, 96986285294151066094112970262797953280
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OFFSET
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5,2
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COMMENTS
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Also number of ways to arrange 5n rooks on an n X n chessboard, with no more than 5 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
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REFERENCES
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B. D. McKay, Applications of a technique for labeled enumeration, Congressus Numerantium, 40 (1983) 207-221.
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LINKS
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FORMULA
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a(n) ~ exp(-1/2)*binomial(n,5)^(2*n) / binomial(n^2,5*n), (Canfield + McKay, 2004)
a(n) ~ sqrt(Pi)*2^(1/2-6*n)*5^(3*n+1/2) *9^(-n)*exp(-5*n-8)*n^(5*n+1/2)
(End)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Michel Buffet (buffet(AT)engref.fr), Oct 08 2002
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EXTENSIONS
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STATUS
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approved
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