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%I #14 Jul 25 2019 03:11:16
%S 1,-1,3,-7,24,-75,285,-1036,4242,-16926,73206,-311256,1403028,
%T -6247527,29082339,-134138290,640672890,-3038045010,14818136190,
%U -71858704710,356665411440,-1761879027090,8874875097270,-44526516209280,227135946200940,-1154738374364100,5955171596514900
%N Moment sequence of tr(A^2) in USp(6).
%C 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 n-th moment of the trace of A^2. See A138542 for central moments.
%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<=g, where F_m(z) = Sum_j binomial(m,j)(B_{(2j-m)/2}(z)-B_{(2j-m+2)/2}(z)) and B_v(z)=0 for non-integer 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.
%e a(4) = 24 because E[(tr(A^2))^4] = 24 for a random matrix A in USp(6).
%Y Cf. A138540, A138542.
%K sign
%O 0,3
%A _Andrew V. Sutherland_, Mar 24 2008
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