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A138542 Central moment sequence of tr(A^2) in USp(6). 1

%I #7 Aug 13 2018 14:25:03

%S 1,0,2,0,11,1,95,36,1099,982,15792,25070,269577,638288,5299294,

%T 16604434,117008255,445625880,2840754502,12378561732,74476435277,

%U 355955681205,2077501474055,10581475229776,60943012224801,324482737520986

%N Central moment sequence of tr(A^2) 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^2+1)^n] is the n-th central moment of the trace of A^2, since E[tr(A^2)] = -1 (see A138541).

%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 A138541.

%e a(5) = 1 because E[(tr(A^2)+1)^5] = 1 for a random matrix A in USp(6).

%Y Cf. A138540, A138541.

%K nonn

%O 0,3

%A _Andrew V. Sutherland_, Mar 24 2008

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