I know that when $X_i$ are independent random variables then wikipedia gives an expression for the excess kurtosis of $\sum_{i=1}^n X_i$. When the $X_i$'s are not independent it just gives a formula for the sum $X+Y$.
I would like to have a general formula for the excess (or simple kurtosis) of a sum of random variables or even better for the sum of Bernoulli 0/1 random variables.