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
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
KEYWORD
nonn
AUTHOR
Andrew V. Sutherland, Mar 24 2008
STATUS
approved