%I M1500
%S 1,2,5,16,67,368,2630,24376,293770,4610624,94080653,2492747656,
%T 85827875506,3842929319936,223624506056156,16901839470598576,
%U 1659776507866213636,211853506422044996288,35137231473111223912310,7569998079873075147860464
%N Number of alternating sign n X n matrices that are symmetric about a diagonal.
%C 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 BousquetMélou, Mireille; and Habsieger, Laurent; Sur les matrices a signes alternants, [On alternatingsign matrices] in Formal power series and algebraic combinatorics (Montreal, PQ, 1992). Discrete Math. 139 (1995), 5772.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. P. Stanley, A baker's dozen of conjectures concerning plane partitions, pp. 285293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
%H D. P. Robbins, Symmetry classes of alternating sign matrices, <a href="http://arXiv.org/abs/math.CO/0008045">arXiv:math.CO/0008045</a>
%H R. P. Stanley, <a href="/A005130/a005130.pdf">A baker's dozen of conjectures concerning plane partitions</a>, pp. 285293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. Preprint. [Annotated scanned copy]
%K nonn,easy,nice
%O 1,2
%A _N. J. A. Sloane_ and _Simon Plouffe_
%E More terms (taken from BousquetMélou & Habsieger's paper) from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008
