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

2,1

Links

Table of n, a(n) for n=2..19.

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A280922, A280921.

Sequence in context: A374982 A003471 A002777 * A118997 A337839 A001257

Adjacent sequences: A280920 A280921 A280922 * A280924 A280925 A280926

Keyword

nonn

Author

Taylor Brysiewicz, Jan 10 2017

Status

approved