I found an online family tree through Ancestry.com that says that Anton Martin born Jan 19, 1823 in Stadtallendorf, Hessen, Germany and was the son of Nicholas Martin and Elisabeth Huhn. Online trees can be a good guide, but should never be taken as gospel until you can do your own research.
I then decided to conduct a little online research of my own.
I went to the 1850 census
Source Citation: Year: 1850; Census Place: Westphalia, Clinton, Michigan; Roll: M432_349; Page: 29; Image: 325.
MARTIN, Nicholas 57 M Farmer Birthplace Germany
Elizabeth 51 F Germany
Lena 21 F Germany
August 18 M Germany
Peter 12 M Germany
Constantine 8 M Michigan
Catherine 6 F Michigan
Living Next Door was
MARTIN Anthony 25 M Farmer Birthplace Germany
Sophia 20 F Germany
Lena 2 F Michigan
It wasn't uncommon in those days for a grown married child to live next door to their parents or other relatives and keep in mind that it was also not uncommon for ages NOT to line up exactly in the census.
Now for the "not so cut and dry"
Also listed down the same page was indeed another "Anthony Martin" family.
MARTIN Anthony 43 M Farmer Birthplace Germany
Lena 39 F Germany
Mary Ann 19 F Germany
Conrad 15 M Germany
Elizabeth 12 F Germany
Caroline 9 F Germany
Joseph 8 M Michigan
Rosina 6 F Michigan
Catherine 1 F Michigan
From the censuses of Nicholas and Anthony (the elder) we can surmise that there is a high likelihood that they were brothers who immigrated to America about the same time (abt 1842) as evidenced bt the births of their children. With Anthony (the younger) living next door to Nicholas, one could see where someone might make the assumption that the younger Anthony was the son of Nicholas. However, I think that there is a strong possibility that the younger Anthony could be the son of Anthony because no only does he carry his name, but the younger Anthony has a daughter named Lena, which is also the name of the older Anthony's wife. However, Nicholas has a daughter also by the name of Lena which leads me to believe that there may be a grandmother who also carries the name.
I think that if we could locate the immigration records for Anthony and Nicholas, we could she more light on this mystery. I've probably muddied the waters much more by now! LOL!!
If you would like a copy of the census page, E-mail me via my profile and send me your E-mail address and I will mail it as an attachment. I hope this helps. Blessings.