Paternal ancestry of Jens Peder Rasmussen
Mads Hansen (father unknown; the first name should be Hans)
Hans Madsen b 1785 (his father is Mads so he’s a Madsen)
Rasmus Hansen b 1825 (his father is Hans so he’s a Hansen)
Jens Peder Rasmussen b 1850 (his father is Rasmus so he’s a Rasmussen) <-----
Does that help?
As you know and as Flemming said, "Kok" is an additional identifier name that can be used with the patronymic name, or not, or sometimes might stand alone as a last name.
Maribo, Fuglse, Sædinge, bemeldte Seddinge, en Gaard, 20, FT-1834, B1231
Hans Madsen 49 Gift Gaardmand og Sognefoged
Ane Kirstine Jørgensdatter 41 Gift hans Kone [Hans Madsen]
Peder Hansen 17 Ugift deres Børn [unmarried, their child]
Else Hansdatter 15 Ugift deres Børn
Rasmus Hansen 8 Ugift deres Børn <----------------------
also shown are three tjenestefolk [hired help]
Peder Larsen 13 Ugift Fattiglem [poor /needy person]
I think Ane Kirstine Jørgensdatter died and Hans remarried to Dorthe Thomsdatter. Is that what you find? If I have that right, this Rasmus Hansen is "your" Rasmus.
Maribo, Fuglse, Sædinge, Seddingegaard, en Gaard, , 37, FT-1845, B5026
Hans Madsen 60 Gift Gaardmand, born in Seddinge
Dorthe Thomsdatter 25 Gift hans Kone, Hillested
Lars Frederik Hansen 5 deres Barn, Seddinge
Karen Hansdatter 3 deres Barn, Seddinge
Rasmus Hansen 20 Ugift deres Barn, Seddinge [their child, born in Seddinge]<-----
- plus 2 tjenestekarl and 2 tjenestepige
Maybe it's possible to find out more about this farm "Seddingegaard."
Below, a family tree showing "Peder Hansen, kaldet [called] Kok/Koch." He's the brother Peter, in 1834 census, above. Maybe Rasmus Hansen was also "kaldet Kok." http://www.oz6ei.dk/2213.htm