It is well known that the sum of squares of all binomial coefficients {n\choose k} with a fixed n is {2n\choose n}. That is, \sum_{k=0}^n {n\choose k}^2 = {2n\choose n}. 

But do we know what the value of the sum of squares of multinomial coefficients is? 
In particular, I am interested in \sum_{a,b,c,d} {n\choose a,b,c,d}^2 , 
where the sum is taken over all 4-tuples {a,b,c,d} of nonnegative integer whose sum is n.

Thanks.