OFFSET
0,5
COMMENTS
Let the random variable X be the coefficient of t^2 in the characteristic polynomial det(tI-A) of a random matrix in USp(6) (6x6 complex matrices that are unitary and symplectic). Then a(n) = E[(X-1)^n] is the n-th central moment of X since E[X]=1 (see A138549).
Dimension of space of invariant tensors in second fundamental representation of Sp(6). - Bruce Westbury, Dec 05 2014
LINKS
Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices, arXiv:0803.4462 [math.NT], 2008-2010.
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k)(-1)^{n-k}*A138549(k).
EXAMPLE
a(4) = 5 because E[(X-1)^4] = 5 for X the t^2 coeff of det(tI-A) in USp(6).
PROG
(LiE) p_tensor(n, [0, 1, 0], C3)|[0, 0, 0]
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew V. Sutherland, Mar 24 2008
STATUS
approved