Search: id:A005163
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%I A005163 M1500
%S A005163 1,2,5,16,67,368,2630,24376,293770,4610624,94080653,2492747656,
%T A005163 85827875506,3842929319936,223624506056156,16901839470598576,
%U A005163 1659776507866213636,211853506422044996288,35137231473111223912310,7569998079873075147860464
%N A005163 Number of alternating sign n X n matrices that are symmetric about a 
               diagonal.
%C A005163 Robbins's paper does not give a formula for this sequence. On the contrary 
               he states: "Apparently these numbers do not factor into small primes, 
               so a simple product formula seems unlikely. Of course this does not 
               rule out other very simple formulas, but these would be more difficult 
               to discover (let alone prove)." As far as I know no formula is currently 
               known. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008
%D A005163 Bousquet-Melou, Mireille; and Habsieger, Laurent; Sur les matrices a 
               signes alternants, [On alternating-sign matrices] in Formal power 
               series and algebraic combinatorics (Montreal, PQ, 1992). Discrete 
               Math. 139 (1995), 57-72.
%D A005163 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005163 R. P. Stanley, A baker's dozen of conjectures concerning plane partitions, 
               pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. 
               Notes Math. 1234, 1986.
%H A005163 D. P. Robbins, Symmetry classes of alternating sign matrices, <a href="http:/
               /arXiv.org/abs/math.CO/0008045">arXiv:math.CO/0008045</a>
%Y A005163 Sequence in context: A019502 A019503 A019504 this_sequence A006116 A122082 
               A002631
%Y A005163 Adjacent sequences: A005160 A005161 A005162 this_sequence A005164 A005165 
               A005166
%K A005163 nonn,easy,nice
%O A005163 1,2
%A A005163 N. J. A. Sloane (njas(AT)research.att.com) and Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005163 More terms (taken from Bousquet-Melou & Habsieger's paper) from Herman 
               Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008

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