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%I #28 Apr 18 2020 22:22:59
%S 1,1,3,55,10147,22069251,602351808741,215717608046511873,
%T 1046591482728407939338275,70417932475495769964322670258947,
%U 66880713903767740581650957184096513655153,909176713758393122455793478657031533216492953328933,178876969166665269546249744608783223036842010760723370462856181,514016665650183402309555825250370336139392333285719205357202846243695510965
%N Number of nonnegative integer matrices of order n for which all row and column sums equal n.
%C Computed by a method that involves summing a multivariate generating function over roots of unity.
%H E. R. Canfield, B. D. McKay, <a href="http://dx.doi.org/10.1007/s00493-010-2426-1">Asymptotic enumeration of integer matrices with large equal row and column sums</a>, Combinatorica 30 (6) (2010) 655-680
%F log a(n) = 2(log 2)*n^2 - n*(log n) - n*(log 4*Pi) + (log n) + O(1). - _Igor Pak_, May 15 2019
%e a(2) = 3 due to the matrices [1,1 | 1,1], [0,2 | 2,0] and [2,0 | 0,2].
%o (Sage)
%o from sage.combinat.integer_matrices import IntegerMatrices
%o [IntegerMatrices([n]*n, [n]*n).cardinality() for n in (0..6)] # _Freddy Barrera_, Dec 27 2018
%Y Cf. A058407, A058410, A058391.
%Y Main diagonal of A257493 and A333901.
%K nonn
%O 0,3
%A _Brendan McKay_, Sep 04 2005
%E a(0)=1 prepended by _Alois P. Heinz_, Apr 26 2015
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