You can have his parents names once more:

Jens Peter Rasmussen
born 23 july 1850 in Sæddinge Parish
baptized at home 4 august
baptized in the church 18 august
Parents: unmarried girl Maren Hansdatter
(father Hans Chr.Pedersen) in Sæddinge, alleged father
bachelor Rasmus Hansen( son of Hans Kok) in Sæddinge.

Maren and Rasmus NEVER married.
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Married 5 march 1854 in Sæddinge Parish.
Bachelor Lars Nielsen,born 24 february 1824,vaccinated 11 july 1825
and
the girl Maren Hansdatter,born 28.september 1821,vaccinated 17 june 1822.

This family in the 1860 census falsterden found is the correct one:

1860
Maribo, Fuglse, Rødby Købstad, Rødby Købstad, 4. Rode, Et Hus, 225,

FT-1860, D6034

Lars Nielsen 35 Gift Arbejdsmand born in Rødby
Maren Hansen 38 Gift Hans Kone b Nebbelunde Sogn, Maribo Amt
Jens Peter Rasmussen 10 Ugift Hendes Søn b Sædinge Sogn, Maribo Amt
Nielsine Andrine Nielsen 6 Ugift Deres Datter b Ringsebølle Sogn, Maribo Amt
Line Nielsen 1 Ugift Deres Datter b Rødby
Frederik Nielsen 3 Ugift Deres Søn b Rødby
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Between 1860 and 1866 the family moved back to Sæddinge Parish.

Maren Hansdatter
died 12 november 1886 in Sæddinge Parish - 65 years old
buried 17 november 1886 in Sæssinge Parish.
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Rasmus Hansens father Hans Madsen Kok died in may 1851 and
in december 1851 Rasmus Hansen moved from Sæddinge Parish
to Hillested Parish.
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Flemming Aasklint