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