

A138541


Moment sequence of tr(A^2) in USp(6).


1



1, 1, 3, 7, 24, 75, 285, 1036, 4242, 16926, 73206, 311256, 1403028, 6247527, 29082339, 134138290, 640672890, 3038045010, 14818136190, 71858704710, 356665411440, 1761879027090, 8874875097270, 44526516209280, 227135946200940, 1154738374364100, 5955171596514900
(list;
graph;
refs;
listen;
history;
text;
internal format)



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^2))^n] is the nth moment of the trace of A^2. See A138542 for central moments.


LINKS

Table of n, a(n) for n=0..26.
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<=g, where F_m(z) = Sum_j binomial(m,j)(B_{(2jm)/2}(z)B_{(2jm+2)/2}(z)) and B_v(z)=0 for noninteger k 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) = 24 because E[(tr(A^2))^4] = 24 for a random matrix A in USp(6).


CROSSREFS

Cf. A138540, A138542.
Sequence in context: A003449 A258308 A148719 * A290750 A148720 A225826
Adjacent sequences: A138538 A138539 A138540 * A138542 A138543 A138544


KEYWORD

sign


AUTHOR

Andrew V. Sutherland, Mar 24 2008


STATUS

approved



