Given: $X_i$ are independent {-1,1} variables with expected value 0 and $X = \sum_{i=1}^n X_i$

Is there a closed form solution / tight bound for $E[ X^{2d} ]$ ?

I realize this problem sounds very simple and may be viewed as a potential homework problem, so I will mention that I'm reading a paper on combinatorial design, involving 2d-independent variables, and I'm trying to take the 2d-th moment of the chebyshev extension.

If you know of a reference, providing the reference (rather than typing out the solution) would suffice.

Thanks!