A280922 Degree of Sp(n,C), the symplectic group, as an algebraic variety.

2, 24, 1744, 769408, 2063048448, 33639061257216, 3336558889746769920, 2013547640260319665029120, 7394216956327379315321530941440, 165246096715086213509958939917335920640, 22475501333841331145301219459764999435840913408

Offset: 1

Author

Taylor Brysiewicz, Jan 10 2017

Keywords

• nonn

Examples

			For n=2 we have a(2)=det({2,4},{4,20})=24.
		

Links

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

Crossrefs

Cf. A103328, A280921, A280923.

Programs

Mathematica

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 *)

PARI

a(n) = matdet(matrix(n,n,i,j,binomial(2*i+2*j-2, 2*i-1))); \\ Michel Marcus, Jan 14 2017

Formula

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

a(n)*2^(2*n) = A280921(2*n+1).

a(n)*2^(2*n+1) = A280923(2*n+1).

Let M_n be the n X n matrix M_n(i,j) = binomial(2*i+2*j-2,2*i-1) = A103328(i+j-1,i-1); then a(n) = det(M_n).