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Search: id:A138542
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| A138542 |
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Central moment sequence of tr(A^2) in USp(6). |
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+0
2
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| 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
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OFFSET
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0,3
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COMMENT
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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
nth central moment of the trace of A^2, since E[tr(A^2)] = -1 (see A138541).
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REFERENCES
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Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials and random matrices", preprint, 2008.
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FORMULA
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mgf is A(z)=e^zF(z) where F(z) is the mgf of A138541.
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EXAMPLE
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a(5) = 1 because E[(tr(A^2)+1)^5] = 1 for a random matrix A in USp(6).
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CROSSREFS
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Cf. A138540, A138541.
Sequence in context: A065624 A086890 A167387 this_sequence A057862 A102869 A075533
Adjacent sequences: A138539 A138540 A138541 this_sequence A138543 A138544 A138545
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KEYWORD
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nonn
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AUTHOR
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Andrew V. Sutherland (drew(AT)math.mit.edu), Mar 24 2008
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