A078524 Numerator of volume of Birkhoff polytope of n X n doubly-stochastic square matrices.
1, 2, 9, 176, 23590375, 9700106723, 77436678274508929033, 5562533838576105333259507434329, 559498129702796022246895686372766052475496691, 727291284016786420977508457990121862548823260052557333386607889
Offset: 1
Examples
Volumes for n=1 to 10, from Beck-Pixton (2003): 1 1 2 2 3 9/8 4 176/2835 5 23590375/167382319104 6 9700106723/1319281996032000000 7 77436678274508929033/13730296368223523839986892800000000 8 5562533838576105333259507434329/1258903626009547795008148094269333980330892800 00000000 9 559498129702796022246895686372766052475496691/9269262340995263649896514671280698429605195132920241960610847715334553600000000000000 10 727291284016786420977508457990121862548823260052557333386607889/828160860106766855125676318796872729344622463533089422677980721388055739956270293750883504892820848640000000
Links
- N. J. A. Sloane, Table of n, a(n) for n = 1..10
- Beck, Matthias, Stanley's Major Contributions to Ehrhart Theory, arXiv preprint arXiv:1407.0255 (2014).
- Matthias Beck and Dennis Pixton, The Ehrhart polynomial of the Birkhoff polytope, Discrete Comput. Geom. 30 (2003), no. 4, 623-637, arXiv:math.CO/0202267
Crossrefs
Extensions
Entry revised by N. J. A. Sloane, Apr 16 2016