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*s-1/2*(s-1)^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) 207-221.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 5..61, (computed with program by Doron Zeilberger, see link below)
B. D. McKay, 0-1 matrices with constant row and column sums
E. R. Canfield and B. D. McKay, Asymptotic enumeration of dense 0-1 matrices with equal row and column sums.
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, Maple package Bipartite.
M. L. Stein and P. R. Stein, Enumeration of Stochastic Matrices with Integer Elements, Report LA-4434, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Jun 1970. [Annotated scanned copy]
FORMULA
From Vaclav Kotesovec, Aug 04 2013: (Start)
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)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Buffet (buffet(AT)engref.fr), Oct 08 2002
EXTENSIONS
More terms from Brendan McKay, Jan 08 2005
STATUS
approved