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 A059475 Number of 2n X 2n half-turn symmetric alternating-sign matrices (HTSASM's). 6
 1, 2, 10, 140, 5544, 622908, 198846076, 180473355920, 465904151957920, 3422048076740462480, 71525763221287897903500, 4254840960508487045451825000, 720428791920558617462950575000000, 347230535542092373572967034254050000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..66 Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5. J. de Gier, Loops, matchings and alternating-sign matrices, arXiv:math/0211285 [math.CO], 2002-2003. 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. G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2001. FORMULA a(n) = A005130(n)*A006366(n). a(n) = A049503(n)*Product_{k=0..n-1} (3*k+2)/(3*k+1). - Seiichi Manyama, Jul 29 2018 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 MATHEMATICA a[n_] := Product[(3k+1)(3k+2)(3k)!^2/(n+k)!^2, {k, 0, n-1}]; Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Sep 01 2018, after Seiichi Manyama *) CROSSREFS Even-numbered terms of A005158. Cf. A005130, A006366, A049503. Sequence in context: A213955 A091990 A014228 * A156296 A003046 A337072 Adjacent sequences: A059472 A059473 A059474 * A059476 A059477 A059478 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 04 2001 STATUS approved

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Last modified April 22 08:40 EDT 2024. Contains 371893 sequences. (Running on oeis4.)