This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A138549 #10 May 10 2019 04:33:20 %S A138549 1,1,2,5,16,62,282,1459,8375,52323,350676,2493846,18659787,145918295, %T A138549 1186129168,9978055080,86545684565,771571356565,7051538798490, %U A138549 65913863945775,628919704903746,6114899366942556,60492393411513722 %N A138549 Moment sequence of t^2 coefficient in det(tI-A) for random matrix A in USp(6). %C A138549 Let the random variable X be the coefficient of t^2 in the characteristic polynomial det(tI-A) of a random matrix in USp(6) (6x6 complex matrices that are unitary and symplectic). Then a(n) = E[X^n]. %C A138549 Let L_p(T) be the L-polynomial (numerator of the zeta function) of a genus 3 curve C. Under a generalized Sato-Tate conjecture, for almost all C, a(n) is the n-th moment of the coefficient of t^2 in L_p(t/sqrt(p)), as p varies. %C A138549 See A138550 for central moments. %H A138549 Kiran S. Kedlaya, Andrew V. Sutherland, <a href="https://arxiv.org/abs/0801.2778">Computing L-series of hyperelliptic curves</a>, arXiv:0801.2778 [math.NT], 2008-2012; Algorithmic Number Theory Symposium--ANTS VIII, 2008. %H A138549 Kiran S. Kedlaya and Andrew V. Sutherland, <a href="http://arXiv.org/abs/0803.4462">Hyperelliptic curves, L-polynomials and random matrices</a>, arXiv:0803.4462 [math.NT], 2008-2010. %H A138549 Nicholas M. Katz and Peter Sarnak, <a href="http://bookstore.ams.org/coll-45/">Random Matrices, Frobenius Eigenvalues and Monodromy</a>, AMS, 1999. %F A138549 See Prop. 12 of first Kedlaya-Sutherland reference. %e A138549 a(3) = 5 because E[X^3] = 5 for X the t^2 coeff of det(tI-A) in USp(6). %Y A138549 Cf. A138540, A138550, A138356. %K A138549 nonn %O A138549 0,3 %A A138549 _Andrew V. Sutherland_, Mar 24 2008