We consider a q-deformation, introduced in [7], of the cumulants associated with a linear functional on polynomials; combinatorially, the deformation is defined using crossing numbers of set-partitions. The paper is concerned with the case q = -1. We show that if the linear functional μ : C[X] → C is symmetric (i.e.μ(Xn) = 0 for n odd), then the exponential generating function of the even (-1)-cumulants of μ is equal to [Formula: see text], (as a formal power series in z). We discuss the connection of this fact with the form of independence for (non-commutative) random variables which corresponds to the operation of Z2-graded tensor product.