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%I M0902 #51 Apr 21 2021 04:42:31
%S 1,2,3,10,25,140,588,5544,39204,622908,7422987,198846076
%N Number of alternating sign n X n matrices invariant under a half-turn.
%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. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986.
%H G. Kuperberg, <a href="https://arxiv.org/abs/math/0008184">Symmetry classes of alternating-sign matrices under one roof</a>, arXiv:math/0008184 [math.CO], 2000-2001.
%H D. P. Robbins, <a href="https://arxiv.org/abs/math/0008045">Symmetry classes of alternating sign matrices, arXiv:math/0008045 [math.CO], 2000.
%H R. P. Stanley, <a href="/A005130/a005130.pdf">A baker's dozen of conjectures concerning plane partitions</a>, pp. 285-293 of "Combinatoire Enumerative (Montreal 1985)", Lect. Notes Math. 1234, 1986. Preprint. [Annotated scanned copy]
%F Robbins gives simple (conjectured) formulas related to this sequence in Section 3.3.
%F a(n) = a(n-1) * (1 + [n even]/3) * C(n\2*3, n\2) / C(n\2*2, n\2) for all n > 1, where C(.,.) are the binomial coefficients, n\2 := floor(n/2) and [n even] = 1 if n is even, 0 else (Iverson bracket). [From Robbins conjectured(!) formulas.] - _M. F. Hasler_, Jun 15 2019
%Y A059475(n) = a(2n).
%K nonn,nice,more
%O 1,2
%A _N. J. A. Sloane_
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