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A286522
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Floor of the volume of the d-th Chern-Vaaler star body.
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5
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2, 4, 8, 14, 23, 36, 52, 72, 93, 116, 138, 158, 174, 185, 191, 191, 186, 176, 162, 146, 128, 110, 93, 77, 62, 49, 38, 29, 22, 16, 12, 8, 6, 4, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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Unimodal: increases from 2 to a maximum of 191, then decreases to 0 = a(d) for d >= 38 (see Grizzard and Gunther, 2016, Lemma 2.2). See A286523 for other comments, references, links, formulas, and programs. For the "monic slice" of the star body, see A288756, A288757, A288758.
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LINKS
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FORMULA
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MATHEMATICA
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a[d_] := (e = Floor[(d-1)/2]; 2^(d+1) (d+1)^e Product[(2k)^(d-2k)/(2k+1)^( d+1-2k), {k, 1, e}]) // Floor;
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PROG
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(PARI) a(n) = floor(2^(n+1)*(n+1)^((n-1)\2)*prod(k=1, (n-1)\2, (2*k)^(n-2*k)/(2*k+1)^(n+1-2*k))); \\ Jinyuan Wang, Mar 05 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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