

A138543


Moment sequence of tr(A^3) in USp(6).


1



1, 0, 3, 0, 26, 0, 345, 0, 5754, 0, 110586, 0, 2341548, 0, 53208441, 0, 1276027610, 0, 31930139670, 0, 826963069140, 0, 22035414489270, 0, 601361536493340, 0, 16749316314679500, 0, 474777481850283240, 0, 13665774112508864385, 0
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OFFSET

0,3


COMMENTS

If A is a random matrix in the compact group USp(6) (6 X 6 complex matrices which are unitary and symplectic), then a(n) = E[(tr(A^3))^n] is the nth moment of the trace of A^3.


LINKS



FORMULA

mgf is A(z) = det[F_{i+j2}(z)], 1<=i,j<=3, where F_m(z) = Sum_j binomial(m,j)(B_{(2jm)/3}(z)B_{(2jm+2)/3}(z)) and B_v(z)=0 for noninteger v and otherwise B_v(z)=I_v(2z) with I_v(z) is the hyperbolic Bessel function (of the first kind) of order v.


EXAMPLE

a(4) = 26 because E[(tr(A^2))^4] = 26 for a random matrix A in USp(6).


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



