

A138546


Moment sequence of tr(A^5) in USp(6).


2



1, 0, 4, 0, 42, 0, 660, 0, 12810, 0, 281736, 0, 6727644, 0, 170316432, 0, 4504487130, 0, 123255492360, 0, 3465702008340, 0, 99645553785960, 0, 2918768920720380, 0, 86852063374902000, 0, 2619552500788984200, 0, 79939673971478231760, 0
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OFFSET

0,3


COMMENTS

If A is a random matrix in the compact group USp(6) (6x6 complex matrices that are unitary and symplectic), then a(n)=E[(tr(A^5))^n] is the nth moment of the trace of A^5.


LINKS

Table of n, a(n) for n=0..31.
Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, Lpolynomials and random matrices, arXiv:0803.4462 [math.NT], 20082010.


FORMULA

mgf is A(z) = det[F_{i+j2}(z)], 1<=i,j<=3, where F_m(z) = Sum_j Binom(m,j)(B_{(2jm)/5}(z)B_{(2jm+2)/5}(z)) and B_v(z)=0 for noninteger v and otherwise B_v(z)=I_v(2z) with I_v(z) the hyperbolic Bessel function (of the first kind) of order v.


EXAMPLE

a(4) = 42 because E[(tr(A^5))^4] = 42 for a random matrix A in USp(6).


CROSSREFS

Cf. A138540.
Sequence in context: A174083 A123936 A271834 * A019217 A221757 A189424
Adjacent sequences: A138543 A138544 A138545 * A138547 A138548 A138549


KEYWORD

nonn


AUTHOR

Andrew V. Sutherland, Mar 24 2008


STATUS

approved



