Expectations of products of quadratic forms in normal variables

Let x be normally distributed N-p(mu, Sigma) where Sigma is positive definite and define the quadratic form Q(x) = x(T)Ax and product Q(k) = Pi(i=1)(k)x(T)A(i)x of quadratic forms. We present explicite simple expressions for the raw moments and cumulants, of arbitrary order, of a quadratic form Q(x) in normal variates on R(p) and of the expectation of a product Q(k) Of an arbitrary number of quadratic forms in normally distributed variables.