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A005158
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Number of alternating sign n X n matrices invariant under a half-turn.
(Formerly M0902)
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4
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1, 2, 3, 10, 25, 140, 588, 5544, 39204, 622908, 7422987, 198846076
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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LINKS
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FORMULA
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Robbins gives simple (conjectured) formulas related to this sequence in Section 3.3.
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
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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STATUS
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approved
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