A138548 Central moment sequence of tr(A^6) in USp(6).

1, 0, 5, 1, 63, 46, 1135, 1800, 25431, 66232, 666387, 2397605, 19650565, 87187842, 633498229, 3214996309, 21829972815, 120665223560, 790528831099, 4613644505799, 29715748525937, 179604102525370, 1149406514424945

Offset

0,3

Comments

If A is a random matrix in the compact group USp(6) (6x6 complex matrices that are unitary and symplectic), then a(n)=E[(tr(A^6)+1)^n] is the n-th central moment of the trace of A^6, since E[tr(A^6)] = -1 (see A138546).

Links

Table of n, a(n) for n=0..22.

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 A138546.

Example

a(5) = 46 because E[(tr(A^6)+1)^5] = 46 for a random matrix A in USp(6).

Crossrefs

Cf. A138540, A138546.

Sequence in context: A246006 A050970 A335955 * A220422 A251596 A294258

Adjacent sequences: A138545 A138546 A138547 * A138549 A138550 A138551

Keyword

nonn

Author

Andrew V. Sutherland, Mar 24 2008

Status

approved