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%I #10 Aug 19 2018 07:35:54
%S 1,0,3,1,27,26,385,708,7231,20296,164277,608565,4286161,19021302,
%T 123867107,617758729,3862576095,20774382552,127548675709,720773229015,
%U 4401180707397,25709943020830,157204921750191,939751281408962
%N Central moment sequence of tr(A^4) in USp(6).
%C If A is a random matrix in the compact group USp(6) (6x6 complex matrices which are unitary and symplectic), then a(n)=E[(tr(A^4+1))^n] is the n-th central moment of the trace of A^4, since E[tr(A^4)] = -1 (see A138544).
%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)=e^zF(z) where F(z) is the mgf of A138544.
%e a(5) = 26 because E[(tr(A^4)+1)^5] = 26 for a random matrix A in USp(6).
%Y Cf. A138544.
%K nonn
%O 0,3
%A _Andrew V. Sutherland_, Mar 24 2008
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