OFFSET
0,3
COMMENTS
If A is a random matrix in the compact group USp(4) (4 X 4 complex matrices which are unitary and symplectic), then a(n)=E[(tr(A^2)^n] is the n-th moment of the trace of A^2. See A138351 for central moments.
LINKS
Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices, Massachusetts Institute of Technology. Dept. of Mathematics.
Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices, arXiv:0803.4462 [math.NT]
FORMULA
EXAMPLE
MATHEMATICA
a[n_] := 1/2*Binomial[2*Floor[n/2]+1, Floor[n/2]+1]*CatalanNumber[1/2*(n+Mod[n, 2])]*(Mod[n, 2]+2); Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Mar 13 2014 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Andrew V. Sutherland, Mar 16 2008
STATUS
approved