

A075754


Number of n X n (0,1) matrices containing exactly five 1's in each row and in each column.


4



1, 720, 3110940, 24046189440, 315031400802720, 6736218287430460752, 226885231700215713535680, 11649337108041078980732943360, 885282776210120715086715619724160, 96986285294151066094112970262797953280
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OFFSET

5,2


COMMENTS

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*s1/2*(s1)^2)*(n*s)^(n*s+1/2)*(s!)^(2*n).  Vaclav Kotesovec, Aug 04 2013


REFERENCES

B. D. McKay, Applications of a technique for labeled enumeration, Congressus Numerantium, 40 (1983) 207221.


LINKS



FORMULA

a(n) ~ exp(1/2)*binomial(n,5)^(2*n) / binomial(n^2,5*n), (Canfield + McKay, 2004)
a(n) ~ sqrt(Pi)*2^(1/26*n)*5^(3*n+1/2) *9^(n)*exp(5*n8)*n^(5*n+1/2)
(End)


CROSSREFS



KEYWORD

nonn


AUTHOR

Michel Buffet (buffet(AT)engref.fr), Oct 08 2002


EXTENSIONS



STATUS

approved



