A078525 Denominator of volume of Birkhoff polytope of n X n doubly-stochastic square matrices.

1, 1, 8, 2835, 167382319104, 1319281996032000000, 13730296368223523839986892800000000, 125890362600954779500814809426933398033089280000000000

Offset

1,3

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.

Example

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

Crossrefs

Numerator is in A078524. See A037302 for more information.

Sequence in context: A017547 A046248 A185901 * A280282 A125539 A297922

Adjacent sequences: A078522 A078523 A078524 * A078526 A078527 A078528

Keyword

nonn,frac,hard

Author

Dean Hickerson, Nov 27 2002

Extensions

Entry revised by N. J. A. Sloane, Apr 16 2016

Status

approved