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 A138541 Moment sequence of tr(A^2) in USp(6). 1
 1, -1, 3, -7, 24, -75, 285, -1036, 4242, -16926, 73206, -311256, 1403028, -6247527, 29082339, -134138290, 640672890, -3038045010, 14818136190, -71858704710, 356665411440, -1761879027090, 8874875097270, -44526516209280, 227135946200940, -1154738374364100, 5955171596514900 (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^2))^n] is the n-th moment of the trace of A^2. See A138542 for central moments. LINKS Table of n, a(n) for n=0..26. 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<=g, where F_m(z) = Sum_j binomial(m,j)(B_{(2j-m)/2}(z)-B_{(2j-m+2)/2}(z)) and B_v(z)=0 for non-integer k 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) = 24 because E[(tr(A^2))^4] = 24 for a random matrix A in USp(6). CROSSREFS Cf. A138540, A138542. Sequence in context: A003449 A258308 A148719 * A290750 A148720 A225826 Adjacent sequences: A138538 A138539 A138540 * A138542 A138543 A138544 KEYWORD sign AUTHOR Andrew V. Sutherland, Mar 24 2008 STATUS approved

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Last modified June 8 13:39 EDT 2023. Contains 363165 sequences. (Running on oeis4.)