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 A138542 #10 Jan 31 2025 03:49:17 %S A138542 1,0,2,0,11,1,95,36,1099,982,15792,25070,269577,638288,5299294, %T A138542 16604434,117008255,445625880,2840754502,12378561732,74476435277, %U A138542 355955681205,2077501474055,10581475229776,60943012224801,324482737520986 %N A138542 Central moment sequence of tr(A^2) in USp(6). %C A138542 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 n-th central moment of the trace of A^2, since E[tr(A^2)] = -1 (see A138541). %H A138542 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. %F A138542 mgf is A(z)=e^zF(z) where F(z) is the mgf of A138541. %e A138542 a(5) = 1 because E[(tr(A^2)+1)^5] = 1 for a random matrix A in USp(6). %Y A138542 Cf. A138540, A138541. %K A138542 nonn %O A138542 0,3 %A A138542 _Andrew V. Sutherland_, Mar 24 2008