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%I #15 Aug 13 2018 09:08:56
%S 4,16,80,768,9536,223232,6867200,393936896,29989282816,4225123221504,
%T 795427838939136,275571189819113472,128240735455510216704,
%U 109332361699222156738560,125729867860804073988096000,263919716304200619134696816640,749827702212803707621023160729600,3876699219598969046471294814225694720
%N Degree of O(n,C), the orthogonal group, as an algebraic variety.
%H M. Brandt, D. Bruce, T. Brysiewicz, R. Krone, E. Robeva, <a href="https://arxiv.org/abs/1701.03200">The degree of SO(n)</a>, arXiv:1701.03200 [math.AG], 2017.
%F a(n) = 2^(n)*det(binomial(2n-2i-2j, n-2i))_{i,j=1..floor(n/2)}.
%F a(n) = 2*A280921(n).
%F a(2n+1) = 2^(2n+1)*A280922(n).
%e For n = 4 we have a(4) = 2^4*det({6,1},{1,1}) = 2^4*(6-1) = 80.
%t a[n_] := 2^n Det[Table[Binomial[2n-2i-2j, n-2i], {i, 1, n/2}, {j, 1, n/2}]]
%t Table[a[n], {n, 2, 19}] (* _Jean-François Alcover_, Aug 12 2018 *)
%o (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
%Y Cf. A280922, A280921.
%K nonn
%O 2,1
%A _Taylor Brysiewicz_, Jan 10 2017
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