A138542 Central moment sequence of tr(A^2) in USp(6).

1, 0, 2, 0, 11, 1, 95, 36, 1099, 982, 15792, 25070, 269577, 638288, 5299294, 16604434, 117008255, 445625880, 2840754502, 12378561732, 74476435277, 355955681205, 2077501474055, 10581475229776, 60943012224801, 324482737520986

Offset

0,3

Comments

If A is a random matrix in the compact group USp(6) (6x6 complex matrices which are unitary and symplectic), then a(n)=E[(tr(A^2+1)^n] is the n-th central moment of the trace of A^2, since E[tr(A^2)] = -1 (see A138541).

Links

Table of n, a(n) for n=0..25.

Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices, arXiv:0803.4462 [math.NT], 2008-2010.

Formula

mgf is A(z)=e^zF(z) where F(z) is the mgf of A138541.

Example

a(5) = 1 because E[(tr(A^2)+1)^5] = 1 for a random matrix A in USp(6).

Crossrefs

Cf. A138540, A138541.

Sequence in context: A189423 A342287 A230696 * A057862 A265512 A102869

Adjacent sequences: A138539 A138540 A138541 * A138543 A138544 A138545

Keyword

nonn

Author

Andrew V. Sutherland, Mar 24 2008

Status

approved