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 A110058 Number of nonnegative integer matrices of order n for which all row and column sums equal n. 3
 1, 1, 3, 55, 10147, 22069251, 602351808741, 215717608046511873, 1046591482728407939338275, 70417932475495769964322670258947, 66880713903767740581650957184096513655153, 909176713758393122455793478657031533216492953328933, 178876969166665269546249744608783223036842010760723370462856181, 514016665650183402309555825250370336139392333285719205357202846243695510965 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A058407, A058410, A058391. Main diagonal of A257493 and A333901. Sequence in context: A172932 A172950 A172962 * A083869 A290773 A119188 Adjacent sequences: A110055 A110056 A110057 * A110059 A110060 A110061 KEYWORD nonn AUTHOR Brendan McKay, Sep 04 2005 EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Apr 26 2015 STATUS approved

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Last modified November 28 02:51 EST 2022. Contains 358406 sequences. (Running on oeis4.)