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A280923
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Degree of O(n,C), the orthogonal group, as an algebraic variety.
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2
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4, 16, 80, 768, 9536, 223232, 6867200, 393936896, 29989282816, 4225123221504, 795427838939136, 275571189819113472, 128240735455510216704, 109332361699222156738560, 125729867860804073988096000, 263919716304200619134696816640, 749827702212803707621023160729600, 3876699219598969046471294814225694720
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OFFSET
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2,1
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LINKS
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M. Brandt, D. Bruce, T. Brysiewicz, R. Krone, E. Robeva, The degree of SO(n), arXiv:1701.03200 [math.AG], 2017.
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FORMULA
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a(n) = 2^(n)*det(binomial(2n-2i-2j, n-2i))_{i,j=1..floor(n/2)}.
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EXAMPLE
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For n = 4 we have a(4) = 2^4*det({6,1},{1,1}) = 2^4*(6-1) = 80.
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MATHEMATICA
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a[n_] := 2^n Det[Table[Binomial[2n-2i-2j, n-2i], {i, 1, n/2}, {j, 1, n/2}]]
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PROG
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(PARI) a(n) = 2^n*matdet(matrix(n\2, n\2, i, j, binomial(2*n-2*i-2*j, n-2*i))); \\ Michel Marcus, Jan 14 2017
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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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