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%I #15 Jul 25 2019 03:10:04
%S 1,-1,6,-15,90,-310,1860,-7455,44730,-195426,1172556,-5416026,
%T 32496156,-156061620,936369720,-4628393055,27770358330,-140348412490,
%U 842090474940,-4331544836190,25989269017140,-135614951248140,813689707488840,-4296741195214650,25780447171287900
%N Moment sequence of tr(A^6) in USp(6).
%C If A is a random matrix in the compact group USp(6) (6 X 6 complex matrices that are unitary and symplectic), then a(n) = E[(tr(A^6))^n] is the n-th moment of the trace of A^6. See A138547 for central moments.
%H Nachum Dershowitz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Dershowitz/dersh3.html">Touchard's Drunkard</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
%H Kiran S. Kedlaya and Andrew V. Sutherland, <a href="http://arXiv.org/abs/0803.4462">Hyperelliptic curves, L-polynomials and random matrices</a>, arXiv:0803.4462 [math.NT], 2008-2010.
%F mgf is A(z) = det[F_{i+j-2}(z)], 1<=i,j<=3, where F_m(z) = Sum_j binomial(m,j)(B_{(2j-m)/6}(z)-B_{(2j-m+2)/6}(z)) and B_v(z)=0 for non-integer 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.
%e a(3) = -15 because E[(tr(A^6))^3] = -15 for a random matrix A in USp(6).
%Y Cf. A138540, A138547.
%K sign
%O 0,3
%A _Andrew V. Sutherland_, Mar 24 2008
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