I did a quick look up for this soldier in the National Parks Service Soldiers and Sailors Database (Google those words to get the URL). Clicking Search for Soldiers, I entered Jacob and Blu, state PA and Union.
The response I got was four different spellings of the same name, all for a man in Co. H, 16th PA Cav (161st Volunteers). The variant spellings were:
Blulinberger
Blulinberger
Bluttenberger
Bluttenberger
These variations are important because his service records could be filed under any or all of those names. Any search for Service records or carded medical records should include all these variant spellings and Blattenberger.
Pennsylvania Service records are not yet digitized on fold3. The compiled carded service records (extracts of the original service records made in the 1880's-90's) and carded medical records (spotty, but reflecting hospitalizations, if they exist) are available at the National Archives in Washington DC. See the NARA website at
www.archives.gov. If you can't go there you can order copies of the records, and as I said, do give all of the above variant spellings including Blattenberger.
I saw no record of a Civil War Pension application on Ancestry or familysearch.org. However, with the difficulty with spelling, I can't be sure he didn't apply -- I didn't search every spelling variant, which you may want to do. If a pension record turns up it will be available at the National Archives, most likely in Washington DC, but some records are in the St Louis branch.
As far as the records go, his regiment probably started out as the 161st Volunteers and later became the 16th PA Cav. The records are now under that designation, properly cited as Co. H, 16th PA (or Penn or Pennsylvania) Cav. (or Cavalry). The word "regiment" or "reg" is not used.
For the history of this battle unit, return to the National Parks Service Soldiers and Sailors Database and click Search Battle Units, enter Pennsylvania, Union and 16th in the appropriate search boxes and choose 16th PA Cav out of the results.
Or if you searched for the soldier on this site, just click on the Regiment next to his name and it will take you to the unit's history and if you like you can browse the complete list of all soldiers in the regiment.
Interestingly, this man appears to be buried as Jacob Blattenberger (3rd letter is an "a"), which may be the correct spelling. You can pick up a lot of family information from his findagrave.com memorial:
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=61357636
Ancestry has more information under Blattenberger. There is a copy if his death certificate, several census records that include him, public family trees, and he was included in the 1890 Veteran's Schedules shoeing residence in Franklin Co PA and that his term of service was 19 Sep 1862 to 17 Jun 1865.
You can get a short free trial of Ancestry and then cancel if you choose not to join (
www.ancestry.com) or visit your local library or check local genealogical or historical societies which may allow free use of Ancestry on their computers if they subscribe. You can search for his records on
www.familysearch.com for free.
Google searches for the soldier and for the regiment might also turn up material of interest.
Good luck. Often Civil War soldiers have fascinating histories. You can use the findagrave memorial and the Ancestry message boards or family trees to try to contact living descendants whoight have letters, photos or diaries. You might also want to check newspaper archives. Good advice on searching historical newspapers appears here in the discussion in the Forum thread Ancestor in Prison During Census.