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Search: id:A138545
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| A138545 |
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Central moment sequence of tr(A^4) in USp(6). |
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+0
3
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| 1, 0, 3, 1, 27, 26, 385, 708, 7231, 20296, 164277, 608565, 4286161, 19021302, 123867107, 617758729, 3862576095, 20774382552, 127548675709, 720773229015, 4401180707397, 25709943020830, 157204921750191, 939751281408962
(list; graph; listen)
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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^4+1))^n] is the
nth central moment of the trace of A^4, since E[tr(A^4)] = -1 (see A138544).
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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 A138544
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EXAMPLE
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a(5) = 26 because E[(tr(A^4)+1)^5] = 26 for a random matrix A in USp(6).
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CROSSREFS
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Cf. 138544.
Adjacent sequences: A138542 A138543 A138544 this_sequence A138546 A138547 A138548
Sequence in context: A033464 A113099 A027495 this_sequence A120066 A046979 A016481
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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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