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A230879 Number of 2-packed n X n matrices.

%I A230879 #20 Oct 08 2017 08:55:21
%S A230879 1,2,56,16064,39156608,813732073472,147662286695991296,
%T A230879 237776857718965784182784,3425329990022686416530808209408,
%U A230879 443021337239562368918979788606843912192,515203019085226443540506018909263027730003787776
%N A230879 Number of 2-packed n X n matrices.
%C A230879 A k-packed matrix of size n X n is a matrix with entries in the alphabet A_k = {0,1, ..., k} such that each row and each column contains at least one nonzero entry.
%H A230879 Andrew Howroyd, <a href="/A230879/b230879.txt">Table of n, a(n) for n = 0..30</a>
%H A230879 H. Cheballah, S. Giraudo, R. Maurice, <a href="http://arxiv.org/abs/1306.6605">Combinatorial Hopf algebra structure on packed square matrices</a>, arXiv preprint arXiv:1306.6605 [math.CO], 2013.
%F A230879 Cheballah et al. give an explicit formula.
%F A230879 a(n) = Sum_{i=0..n} Sum_{j=0..n} (-1)^(i+j) * binomial(n,i) * binomial(n,j) * 3^(i*j). - _Andrew Howroyd_, Sep 20 2017
%t A230879 p[k_, n_] := Sum[(-1)^(i + j)*Binomial[n, i]*Binomial[n, j]*(k + 1)^(i*j), {i, 0, n}, {j, 0, n}];
%t A230879 a[n_] := p[2, n];
%t A230879 Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Oct 08 2017, translated from PARI *)
%o A230879 (PARI) \\ here p(k,n) is number of k-packed matrices of size n.
%o A230879 p(k,n)={sum(i=0, n, sum(j=0, n, (-1)^(i+j) * binomial(n,i) * binomial(n,j) * (k+1)^(i*j)))}
%o A230879 a(n) = p(2,n); \\ _Andrew Howroyd_, Sep 20 2017
%Y A230879 Row sums of A230878.
%Y A230879 Cf. A048291, A055599, A230880, A104602.
%K A230879 nonn
%O A230879 0,2
%A A230879 _N. J. A. Sloane_, Nov 09 2013
%E A230879 Terms a(7) and beyond from _Andrew Howroyd_, Sep 20 2017