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 A138542 Central moment sequence of tr(A^2) in USp(6). 1
 1, 0, 2, 0, 11, 1, 95, 36, 1099, 982, 15792, 25070, 269577, 638288, 5299294, 16604434, 117008255, 445625880, 2840754502, 12378561732, 74476435277, 355955681205, 2077501474055, 10581475229776, 60943012224801, 324482737520986 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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). LINKS Table of n, a(n) for n=0..25. Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices, arXiv:0803.4462 [math.NT], 2008-2010. FORMULA mgf is A(z)=e^zF(z) where F(z) is the mgf of A138541. EXAMPLE a(5) = 1 because E[(tr(A^2)+1)^5] = 1 for a random matrix A in USp(6). CROSSREFS Cf. A138540, A138541. Sequence in context: A189423 A342287 A230696 * A057862 A265512 A102869 Adjacent sequences: A138539 A138540 A138541 * A138543 A138544 A138545 KEYWORD nonn AUTHOR Andrew V. Sutherland, Mar 24 2008 STATUS approved

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Last modified June 9 09:54 EDT 2023. Contains 363178 sequences. (Running on oeis4.)