%I A008793
%S A008793 1,2,20,980,232848,267227532,1478619421136,39405996318420160,
%T A008793 5055160684040254910720,3120344782196754906063540800,
%U A008793 9265037718181937012241727284450000,132307448895406086706107959899799334375000
%N A008793 Number of ways to tile hexagon of edge n with diamonds of side 1. Also 
               number of plane partitions whose Young diagrams fit inside an n X 
               n X n box.
%D A008793 Gordon G. Cash and Jerry Ray Dias, Computation, Properties and Resonance 
               Topology of Benzenoid Monoradicals and Polyradicals and the Eigenvectors 
               Belonging to Their Zero Eigenvalues, J. Math. Chem., 30 (2001), 429-444. 
               [See K, p. 442.]
%D A008793 J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 
               in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, 
               Cambridge, 1999 (see p. 261).
%H A008793 T. D. Noe, <a href="b008793.txt">Table of n, a(n) for n=0..30</a>
%H A008793 P. Di Francesco, P. Zinn-Justin and J.-B. Zuber, <a href="http://arXiv.org/
               abs/math-ph/0410002">Determinant formulae for some tiling problems...</
               a>
%H A008793 I. Fischer, <a href="http://arXiv.org/abs/math.CO/9906102">[math/9906102] 
               Enumeration of rhombus tilings of a hexagon which contain a fixed 
               rhombus in the center</a>
%H A008793 P. J. Forrester and A. Gamburd, <a href="http://arXiv.org/abs/math.CO/
               0503002">Counting formulas associated with some random matrix averages</
               a>
%H A008793 M. Fulmek and C. Krattenthaler, <a href="http://arXiv.org/abs/math.CO/
               9909038">[math/9909038] The number of rhombus tilings of a symmetric 
               hexagon which contain a fixed rhombus on the symmetry axis, II</a>
%H A008793 H. Helfgott and I. M. Gessel, <a href="http://arXiv.org/abs/math.CO/9810143">
               Enumeration of tilings of diamonds and hexagons with defects</a>
%H A008793 J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera 
               et al. (eds.), <a href="http://www.msri.org/publications/books/Book38/
               contents.html">New Perspectives in Algebraic Combinatorics</a>
%H A008793 J. Propp, <a href="http://math.wisc.edu/~propp/update.ps.gz">Updated 
               article</a>
%H A008793 N. C. Saldanha and C. Tomei, <a href="http://arXiv.org/abs/math.CO/9801111">
               [math/9801111] An overview of domino and lozenge tilings</a>
%H A008793 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PlanePartition.html">Link to a section of The World of Mathematics.</
               a>
%F A008793 Product_{i=0..n-1} (i^(-i)*(n+i)^(2i-n)*(2n+i)^(n-i)).
%F A008793 Product_{i=1..n} Product_{j=0..n-1} (3*n-i-j)/(2*n-i-j).
%F A008793 Product[Gamma[i]Gamma[i+2n]/Gamma[i+n]^2, {i, n}
%F A008793 Product[i=0..n-1, i!(i+2n)!/(i+n)!^2 ].
%F A008793 a(n)=Prod[i=1..n, Prod[j=n..2n-1, i+j]/Prod[j=0..n-1, i+j]]; - Paul Barry 
               (pbarry(AT)wit.ie), Jun 13 2006
%p A008793 A008793 := proc(n) local i; mul((i - 1)!*(i + 2*n - 1)!/((i + n - 1)!)^2, 
               i = 1 .. n) end proc;
%t A008793 Table[ Product[ (i+j+k-1)/(i+j+k-2), {i, n}, {j, n}, {k, n} ], {n, 10} 
               ]
%Y A008793 Cf. A066931. Main diagonal of array A103905.
%Y A008793 Sequence in context: A006547 A135757 A158843 this_sequence A015192 A012790 
               A013144
%Y A008793 Adjacent sequences: A008790 A008791 A008792 this_sequence A008794 A008795 
               A008796
%K A008793 nonn,easy,nice
%O A008793 0,2
%A A008793 Jonas Wallgren (jwc(AT)ida.liu.se)
%E A008793 More terms from Eric Weisstein (eric(AT)weisstein.com)