%I #15 Sep 27 2016 14:27:30

%S 1,1,8,2835,167382319104,1319281996032000000,

%T 13730296368223523839986892800000000,

%U 125890362600954779500814809426933398033089280000000000

%N Denominator of volume of Birkhoff polytope of n X n doubly-stochastic square matrices.

%H N. J. A. Sloane, <a href="/A078525/b078525.txt">Table of n, a(n) for n = 1..10</a>

%H Beck, Matthias, <a href="http://arxiv.org/abs/1407.0255">Stanley's Major Contributions to Ehrhart Theory</a>, arXiv preprint arXiv:1407.0255 (2014).

%H Matthias Beck and Dennis Pixton, <a href="http://arxiv.org/abs/math/0202267">The Ehrhart polynomial of the Birkhoff polytope</a>, Discrete Comput. Geom. 30 (2003), no. 4, 623-637, arXiv:math.CO/0202267.

%e Volumes for n=1 to 10, from Beck-Pixton (2003):

%e 1 1

%e 2 2

%e 3 9/8

%e 4 176/2835

%e 5 23590375/167382319104

%e 6 9700106723/1319281996032000000

%e 7 77436678274508929033/13730296368223523839986892800000000

%e 8 5562533838576105333259507434329/1258903626009547795008148094269333980330892800

%e 00000000

%e 9 559498129702796022246895686372766052475496691/9269262340995263649896514671280698429605195132920241960610847715334553600000000000000

%e 10 727291284016786420977508457990121862548823260052557333386607889/828160860106766855125676318796872729344622463533089422677980721388055739956270293750883504892820848640000000

%Y Numerator is in A078524. See A037302 for more information.

%K nonn,frac,hard

%O 1,3

%A _Dean Hickerson_, Nov 27 2002

%E Entry revised by _N. J. A. Sloane_, Apr 16 2016