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 A138543 Moment sequence of tr(A^3) in USp(6). 1
 1, 0, 3, 0, 26, 0, 345, 0, 5754, 0, 110586, 0, 2341548, 0, 53208441, 0, 1276027610, 0, 31930139670, 0, 826963069140, 0, 22035414489270, 0, 601361536493340, 0, 16749316314679500, 0, 474777481850283240, 0, 13665774112508864385, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS If A is a random matrix in the compact group USp(6) (6 X 6 complex matrices which are unitary and symplectic), then a(n) = E[(tr(A^3))^n] is the n-th moment of the trace of A^3. LINKS Table of n, a(n) for n=0..31. 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) = det[F_{i+j-2}(z)], 1<=i,j<=3, where F_m(z) = Sum_j binomial(m,j)(B_{(2j-m)/3}(z)-B_{(2j-m+2)/3}(z)) and B_v(z)=0 for non-integer v and otherwise B_v(z)=I_v(2z) with I_v(z) is the hyperbolic Bessel function (of the first kind) of order v. EXAMPLE a(4) = 26 because E[(tr(A^2))^4] = 26 for a random matrix A in USp(6). CROSSREFS Cf. A138540. Sequence in context: A057379 A360063 A009777 * A238104 A143769 A190963 Adjacent sequences: A138540 A138541 A138542 * A138544 A138545 A138546 KEYWORD nonn AUTHOR Andrew V. Sutherland, Mar 24 2008 STATUS approved

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Last modified June 10 16:26 EDT 2023. Contains 363205 sequences. (Running on oeis4.)