A138545 Central moment sequence of tr(A^4) in USp(6).

1, 0, 3, 1, 27, 26, 385, 708, 7231, 20296, 164277, 608565, 4286161, 19021302, 123867107, 617758729, 3862576095, 20774382552, 127548675709, 720773229015, 4401180707397, 25709943020830, 157204921750191, 939751281408962

Offset

0,3

Comments

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^4+1))^n] is the n-th central moment of the trace of A^4, since E[tr(A^4)] = -1 (see A138544).

Links

Table of n, a(n) for n=0..23.

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)=e^zF(z) where F(z) is the mgf of A138544.

Example

a(5) = 26 because E[(tr(A^4)+1)^5] = 26 for a random matrix A in USp(6).

Crossrefs

Cf. A138544.

Sequence in context: A271128 A271163 A270017 * A271806 A270289 A344037

Adjacent sequences: A138542 A138543 A138544 * A138546 A138547 A138548

Keyword

nonn

Author

Andrew V. Sutherland, Mar 24 2008

Status

approved