OFFSET
0,3
COMMENTS
Computed by a method that involves summing a multivariate generating function over roots of unity.
LINKS
E. R. Canfield, B. D. McKay, Asymptotic enumeration of integer matrices with large equal row and column sums, Combinatorica 30 (6) (2010) 655-680
FORMULA
log a(n) = 2(log 2)*n^2 - n*(log n) - n*(log 4*Pi) + (log n) + O(1). - Igor Pak, May 15 2019
EXAMPLE
a(2) = 3 due to the matrices [1,1 | 1,1], [0,2 | 2,0] and [2,0 | 0,2].
PROG
(Sage)
from sage.combinat.integer_matrices import IntegerMatrices
[IntegerMatrices([n]*n, [n]*n).cardinality() for n in (0..6)] # Freddy Barrera, Dec 27 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Brendan McKay, Sep 04 2005
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Apr 26 2015
STATUS
approved