A280923 Degree of O(n,C), the orthogonal group, as an algebraic variety.

4, 16, 80, 768, 9536, 223232, 6867200, 393936896, 29989282816, 4225123221504, 795427838939136, 275571189819113472, 128240735455510216704, 109332361699222156738560, 125729867860804073988096000, 263919716304200619134696816640, 749827702212803707621023160729600, 3876699219598969046471294814225694720

Offset: 2

Author

Taylor Brysiewicz, Jan 10 2017

Keywords

• nonn

Examples

			For n = 4 we have a(4) = 2^4*det({6,1},{1,1}) = 2^4*(6-1) = 80.
		

Links

• M. Brandt, D. Bruce, T. Brysiewicz, R. Krone, E. Robeva, The degree of SO(n), arXiv:1701.03200 [math.AG], 2017.

Crossrefs

Cf. A280922, A280921.

Programs

Mathematica

a[n_] := 2^n Det[Table[Binomial[2n-2i-2j, n-2i], {i, 1, n/2}, {j, 1, n/2}]]
Table[a[n], {n, 2, 19}] (* Jean-François Alcover, Aug 12 2018 *)

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

Formula

a(n) = 2^(n)*det(binomial(2n-2i-2j, n-2i))_{i,j=1..floor(n/2)}.

a(n) = 2*A280921(n).

a(2n+1) = 2^(2n+1)*A280922(n).