A280922
Degree of Sp(n,C), the symplectic group, as an algebraic variety.
Original entry on oeis.org
2, 24, 1744, 769408, 2063048448, 33639061257216, 3336558889746769920, 2013547640260319665029120, 7394216956327379315321530941440, 165246096715086213509958939917335920640, 22475501333841331145301219459764999435840913408
Offset: 1
For n=2 we have a(2)=det({2,4},{4,20})=24.
- 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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a[n_] := Det[Table[Binomial[2i+2j-2, 2i-1], {i, 1, n}, {j, 1, n}]]
Table[a[n], {n, 1, 11}] (* Jean-François Alcover, Aug 12 2018 *)
-
a(n) = matdet(matrix(n,n,i,j,binomial(2*i+2*j-2, 2*i-1))); \\ Michel Marcus, Jan 14 2017
A280923
Degree of O(n,C), the orthogonal group, as an algebraic variety.
Original entry on oeis.org
4, 16, 80, 768, 9536, 223232, 6867200, 393936896, 29989282816, 4225123221504, 795427838939136, 275571189819113472, 128240735455510216704, 109332361699222156738560, 125729867860804073988096000, 263919716304200619134696816640, 749827702212803707621023160729600, 3876699219598969046471294814225694720
Offset: 2
For n = 4 we have a(4) = 2^4*det({6,1},{1,1}) = 2^4*(6-1) = 80.
- 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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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 *)
-
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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