Luca Trevisan [here][1] gives a randomized polynomial-time approximation algorithm for #3-coloring given an NP oracle.

 In a similar vein, I was wondering if there were any results on $BPP^{NP}\stackrel{?}{=}$ #P - i.e. outputting a correct count for a #P problem under the presence of an NP oracle with high probability.
 If not, then is $BPP^{NP}$ believed to be equal to #P? 

 [1]: http://lucatrevisan.wordpress.com/2008/02/16/approximate-counting/


Thanks