You've probably long since moved on, but, just for reference, the 
initial conditions HORIZONS uses are mentioned ("header.431_572") in 
ftp://ssd.jpl.nasa.gov/pub/eph/planets/Linux/README.txt but the only 
place I could find them in "table form" is in my own git repository: 
 
https://github.com/barrycarter/bcapps/blob/master/ASTRO/header.431_572 
 
The values are explained in 
http://ilrs.gsfc.nasa.gov/docs/2014/196C.pdf starting on page 39, 
"VI. Initial Conditions and Constants", especially in the tables 
starting with Table 4 on page 47 and ending with Table 13 on page 74. 
 
I've written scripts to setup the initial conditions and numerically 
solve the differential equations using Mathematica, so the following 
may be helpful: 
 
https://github.com/barrycarter/bcapps/blob/master/ASTRO/README

https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-header-values.pl 

https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-integrate.m

The output of the Perl script above, which includes all the equations you'll need, is: https://github.com/barrycarter/bcapps/tree/master/ASTRO/bc-integrate-init.m

 
When I reduce the step size sufficiently (Mathematica's default step 
size is too large), my results closely match those of HORIZONS: 
 
https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-integrate-compare.m