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A280923 Degree of O(n,C), the orthogonal group, as an algebraic variety. 2
4, 16, 80, 768, 9536, 223232, 6867200, 393936896, 29989282816, 4225123221504, 795427838939136, 275571189819113472, 128240735455510216704, 109332361699222156738560, 125729867860804073988096000, 263919716304200619134696816640, 749827702212803707621023160729600, 3876699219598969046471294814225694720 (list; graph; refs; listen; history; text; internal format)
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: A279361 A003471 A002777 * A118997 A337839 A001257

Adjacent sequences:  A280920 A280921 A280922 * A280924 A280925 A280926

KEYWORD

nonn

AUTHOR

Taylor Brysiewicz, Jan 10 2017

STATUS

approved

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Last modified September 27 19:23 EDT 2021. Contains 347694 sequences. (Running on oeis4.)