%I A138354
%S A138354 1,0,3,1,21,26,215,498,2821,9040,43695,165375,752785,3101970,13881803,
%T A138354 59837183,267860685,1184749704,5337504263,23996776941,108964583121,
%U A138354 495544446410,2267450194443,10402298479276,47926692348121
%N A138354 Central moment sequence of tr(A^4) in USp(4).
%C A138354 Binomial transform of A018224.
%C A138354 If A is a random matrix in the compact group USp(4) (4 X 4 complex 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 A018224).
%D A138354 Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials 
               and random matrices", preprint, 2008.
%H A138354 Kiran S. Kedlaya and Andrew V. Sutherland, <a href="http://arXiv.org/
               abs/0803.4462">Hyperelliptic curves, L-polynomials and random matrices</
               a>.
%F A138354 a(n)=(1/2)Integral_{x=0..Pi,y=0..Pi}(2cos(4x)+2cos(4y)+1)^n(2cos(x)-2cos(y))^2(2/
               Pi*sin^2(x))(2/Pi*sin^2(y))dxdy. a(n)=Sum_{i=0..n}binomial(n,i)A018224(i).
%e A138354 a(3) = 1 because E[(tr(A^4)+1)^3] = 1.
%e A138354 a(3) = 1*A018224(0) + 3*A018224(1) + 3*A018224(2) + 1*A018224(1)
%e A138354 = 1*1 + 3*(-1) + 3*4 + 1*(-9) = 1.
%Y A138354 Cf. A018224.
%Y A138354 Sequence in context: A000369 A136236 A113090 this_sequence A010291 A027477 
               A137330
%Y A138354 Adjacent sequences: A138351 A138352 A138353 this_sequence A138355 A138356 
               A138357
%K A138354 nonn
%O A138354 0,3
%A A138354 Andrew V. Sutherland (drew(AT)math.mit.edu), Mar 16 2008, Mar 31 2008