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Search: id:A059477
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| A059477 |
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3-enumeration of n X n alternating-sign matrices. |
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1
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| 1, 1, 2, 9, 90, 2025, 102060, 11573604, 2946308904, 1687603650084, 2171945897658108, 6289412333143466241, 40940643700218614247324, 599627833263501883888374756, 19747212169938041691404746667280, 1463229065460461810019231236067824400
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv math.CO/0008184
F. Colomo and A. G. Pronko, On the refined 3-enumeration of alternating sign matrices.
F. Colomo and A. G. Pronko, On the refined 3-enumeration of alternating sign matrices, Advances in Applied Mathematics 34 (2005) 798.
F. Colomo and A. G. Pronko, Square ice, alternating sign matrices and classical orthogonal polynomials, JSTAT (2005) P01005.
Yu. G. Stroganov, 3-enumerated alternating sign matrices, math-ph/0304004.
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FORMULA
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a(2m+1)=3^(m*(m+1))*prod(k=1, m, ((3*k-1)!/(m+k)!)^2), a(2m+2)=3^m*(3*m+2)!*m!/((2*m+1)!)^2*a(2m+1). - R. Stephan, Apr 24 2004
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MAPLE
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A059477 := proc(n) local i, j, t1; t1 := 3^(n^2-n)*2^(-n^2+n); for i from 1 to n do for j from 1 to n do if j-i mod 2 <> 0 then t1 := t1*(3*j-3*i+1)/(3*j-3*i); fi; od; od; t1; end;
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CROSSREFS
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Cf. A005130.
Sequence in context: A001192 A006120 A012941 this_sequence A136553 A011804 A058156
Adjacent sequences: A059474 A059475 A059476 this_sequence A059478 A059479 A059480
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 04 2001
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