In the OEIS [index][1], see  
"McKay-Thompson sequences or series for Monster simple group, sequences related to"  

These may come with tables of coefficients, and with programs to compute coefficients.  [If you understand how "replicable" series work, you can program your own.]  

When was working on related things, when I computed long lists of the coefficients, I added them to the OEIS database.  Others do the same, so it is improving all the time.

  [1]: http://oeis.org/wiki/Index_to_OEIS:_Section_Mat