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%I A029894 #26 Nov 01 2019 12:34:49
%S A029894 1,2,7,34,221,1736,15584,153228,1611189,17826202,205282376,2441437708,
%T A029894 29816628471,372314544202,4737438631001,61264426341926,
%U A029894 803488037899349,10668478221202710,143203795004873285,1940953294927992976,26536578116407809962,365653739580163294032
%N A029894 Number of directed (or Gale-Ryser) graphical partitions: degree-vector pairs (in-degree, out-degree) for directed graphs (loops allowed) with n vertices; or possible ordered pair (row-sum, column-sum) vectors for a 0-1 matrix.
%D A029894 R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.
%H A029894 Andrew Howroyd, <a href="/A029894/b029894.txt">Table of n, a(n) for n = 0..30</a>
%H A029894 Peter L. Erdos, I Miklós, Z Toroczkai, <a href="http://arxiv.org/abs/1601.08224">New classes of degree sequences with fast mixing swap Markov chain sampling</a>, arXiv preprint arXiv:1601.08224 [math.CO], 2016.
%H A029894 <a href="/index/Gra#graph_part">Index entries for sequences related to graphical partitions</a>
%F A029894 Calculated using Cor. 6.3.3, Th. 6.3.6, Cor. 6.2.5 of Brualdi-Ryser.
%F A029894 a(n) = F(n, n, 0, n) where F(b, c, t, w) = Sum_{i=0..b} Sum_{j=ceiling((t+i)/w))..min(t+i, c)} F(i, j, t+i-j, w-1) for w > 0, F(b, c, 0, 0) = 1 and F(b, c, t, 0) = 0 for t > 0. - _Andrew Howroyd_, Nov 01 2019
%o A029894 (PARI) \\ see A327913 for T(n,m)
%o A029894 for(n=0, 15, print1(T(n,n), ", ")) \\ _Andrew Howroyd_, Nov 01 2019
%Y A029894 Main diagonal of A327913.
%Y A029894 Cf. A000569, A004250, A004251, A029889, A318396.
%K A029894 nonn
%O A029894 0,2
%A A029894 torsten.sillke(AT)lhsystems.com
%E A029894 "Loops allowed" added to the definition by _Brendan McKay_, Oct 20 2015
%E A029894 a(0)=1 prepended and terms a(12) and beyond from _Andrew Howroyd_, Oct 31 2019

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