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%I #7 Aug 13 2018 14:25:45
%S 1,0,5,1,63,46,1135,1800,25431,66232,666387,2397605,19650565,87187842,
%T 633498229,3214996309,21829972815,120665223560,790528831099,
%U 4613644505799,29715748525937,179604102525370,1149406514424945
%N Central moment sequence of tr(A^6) in USp(6).
%C 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^6)+1)^n] is the n-th central moment of the trace of A^6, since E[tr(A^6)] = -1 (see A138546).
%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 A138546.
%e a(5) = 46 because E[(tr(A^6)+1)^5] = 46 for a random matrix A in USp(6).
%Y Cf. A138540, A138546.
%K nonn
%O 0,3
%A _Andrew V. Sutherland_, Mar 24 2008
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