How to remove double for loop?

Hello everyone.

I use double for loops to fill in matrices, but there are surely
better (and computationally faster) ways to perform that task.
Could someone show me, given the following example of a double for
loop, how this could be done? It is much easier to learn by examples.

Val <- matrix(0, nrow=n+1, ncol=n+1)
for( i in 0:n){
    for(j in 0:i){
        Val[j+1, i+1] <- u^j*d^(i-j)
    }
}

Thank you in advance!

Jonas Malmros