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A059475
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Number of 2n X 2n half-turn symmetric alternating-sign matrices (HTSASM's).
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6
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1, 2, 10, 140, 5544, 622908, 198846076, 180473355920, 465904151957920, 3422048076740462480, 71525763221287897903500, 4254840960508487045451825000, 720428791920558617462950575000000, 347230535542092373572967034254050000000
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OFFSET
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0,2
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LINKS
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Heuer, Dylan, Chelsey Morrow, Ben Noteboom, Sara Solhjem, Jessica Striker, and Corey Vorland. "Chained permutations and alternating sign matrices - Inspired by three-person chess." Discrete Mathematics 340, no. 12 (2017): 2732-2752. Also arXiv:1611.03387.
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FORMULA
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a(n) ~ exp(1/18) * Gamma(1/3)^(2/3) * n^(1/18) * 3^(3*n^2 + 1/9) / (A^(2/3) * Pi^(1/3) * 2^(4*n^2 + 1/6)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jan 26 2020
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MATHEMATICA
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a[n_] := Product[(3k+1)(3k+2)(3k)!^2/(n+k)!^2, {k, 0, n-1}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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