login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A138550
Central moment sequence of t^2 coefficient in det(tI-A) for random matrix A in USp(6).
2
1, 0, 1, 1, 5, 16, 75, 366, 2016, 11936, 75678, 507575, 3575693, 26289408, 200709665, 1584482382, 12888498820, 107698656192, 922140333952, 8072379904752, 72108967554160, 656190909218560, 6074106708205200, 57118680813847840
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
STATUS
approved