The marriage record for Karen Nikolaisdatter and Erik Martinussen states her father's name to be NIkolai Olsen of Barbo.
The information below is based on two original records that can be viewed. One I have copied below.
Norway, Church Records, 1812-1938
Detail Source
Name Karen Nikolaisdatter
Marriage Age 30
Record Type ekteskap (Marriage)
Birth Date abt 1845
Birth Place Barbo
Marriage Date 16 jun 1875
Marriage Place Orkdal, Sør-Trøndelag, Norge (Norway)
Marriage Municipality Orkland
Father Nikolai Olsen Barbo
Spouse Erik Martinussen
Names in Norway can be a dilemma in that the person may have the father's first name with "sen" or "datter" added (most common in old records), or the father's last name, or the name of the place they were born or were living in order to differentiate them from other people with the same name, or their married name is the name in records. In this case I can't find the (Nikkolai) Olsen name associated with Nikolai Pedersen. Nikolai's father was Peder Nikolaisen -- had it been Olsen I may not have questioned this. I hesitate to develop Nikolai Pedersen further in my tree as Karen's father. If Karen had been born before the marriage of Nikolai and Andrea, I would not question the Olsen name, but they were married in 1840 and Karen was born from 1841-1845. I am still searching for her birth record. Does anyone have some input for this? Thank you.