If you have an exploding N-sided die that adds another die when it's at max, the average A is:
A = (1+2+...N+A)/N
This is the same as:
A = (N(N+1) + A)/2N
This, in turn, can be simplified to:
2N*A = N(N+1) + A
And that in turn, can be simplified to what Pat Ludwig has so kindly tabulated.
A similar method can be used to calculate averages when the highest roll of a die is substituted by tolling 2 (or more) of the same dice-type.