Here are Jacob Andersen and his wife Maren Jensen, on the 1860 census in Sjellerup, Denmark. Matching what Maren's obituary indicated.

Præstø, Fakse, Spjellerup, Spjellerup by, , en Gaard, 5, FT-1860
Name: Age: Marital status: Occupation in household: Occupation: Birth place:
The farm owner and his wife:
Jens Pedersen 67 Gift gaardejer. Thureby sogn, Præstø amt
Kirsten Olsdatter 63 Gift Hans kone Varpelev sogn, Præstø amt.
The couple that came to Douglas County, Minnesota in 1870:
Jacob Andersen 24 Married farmworker. Karise parish, Præstø county, Sjælland, Denmark.
Maren Jensen 26 Married, his wife, born in Spjellerup parish, Præstø county, Sjælland, Denmark
Hired farm hands, unmarried
Hans Andersen 22 Ugift Tjenestefolk Karise sogn, Præstø amt
Rasmus Jensen 16 Ugift Tjenestefolk Spjellerup sogn, Præstø amt
Maren Kirstine Larsen 23 Ugift Tjenestefolk Faxe sogn, Præstø amt.

1875 census:
https://familysearch.org/pal:/MM9.1.1/MKN8-MJX

name: Jacob Andersen
residence: Osakis, Douglas, Minnesota
age: 38
estimated birth year: 1837
father's birthplace: Denmark
mother's birthplace: Denmark
birthplace: Denmark
race: White
gender: Male
line number: 29
family number: 81
film number: 0565718
Household Gender Age Birthplace
Jacob Andersen M Denmark
Mary Andersen F Denmark
Mary Andersen F Denmark
Anna Andersen F Denmark
Charles Robertson M Denmark

1880 census:
name : Jacob Anderson
event: Census
event date: 1880
event place: Osakis, Douglas, Minnesota, United States
gender: Male
age: 44
marital status : Married
occupation : Farmer
race or color (original) :
ethnicity (standardized) : American
relationship to head : Self
birthplace : Denmark
birthdate : 1836
spouse's name : Mary Anderson
spouse's birthplace : Denmark
father's name :
father's birthplace : Denmark
mother's name :
mother's birthplace : Denmark
page : 503
page character : D
entry number : 532
nara film number : T9-0618
gs film number : 1254618
digital folder number: 004242000
image number: 00694
Household Gender Age Birthplace
self Jacob Anderson M 44 Denmark
wife Mary Anderson F 46 Denmark
daughter Maria Anderson F 18 Denmark
daughter Stine Anderson F 4 Minnesota, United States
other Patrick Connelly M 35 Ireland
other Micheal Mccarney M 35 Ireland
other Edward Porter M 24 England
other Richard Fitzgerald M 25 England

1885 census:
https://familysearch.org/pal:/MM9.1.1/MQXC-YXC
name: Jacob Anderson
residence: Alexandria, Douglas, Minnesota
age: 48 years
estimated birth year: 1837
birthplace: Denmark
race: White
gender: Male
family number: 320
volume: Douglas
page number: 20
film number: 000565737
Household Gender Age Birthplace
Jacob Anderson M 48y Denmark
Maren Anderson F 50y Denmark
Mam Anderson F 23y Denmark
St* Anderson F 9y Minnesota
Marie Anderson F 15y Minnesota
Anna Anderson F 9y Minnesota
W L Hogan M 36y Maryland
Augusta Anderson F 15y Sweden
H P James M Vermont
Danl Walker M 35y Canada
A F Reemer M 22y Germany
Hanson M 26y Denmark
G R Morse M 27y Ohio
Oscar Halvorson M 15y Minnesota

Spjellerup, Denmark.
See wife Maren's listing (link below) for marriage and emigration information.

Obituary:
Obituary – Alexandria Citizen news, Sept. 22, 1904
Jacob Anderson (should be Andersen)
The hand of death has been laid upon another of Douglas County's pioneers. This time it is Jacob Anderson, well-known in nearly every section of the county. After a sickness of about 5 months, he succumbed Friday morning at 6:30 to the ravages of Bright's Disease (Kidney failure). Mr. Anderson was born in Karisa, Denmark, November 29, 1836, being at the time of his death nearly 68 years of age. He came to this country in 1870, returning to Denmark the same year, where he remained 2 years andthen came to this country to live in 1873, locating at Nelson Station, where he lived for 11 years. He then moved to Alexandria and bought the Minnesota House, which he ran for 20 years. During this time he bought a farm in Osakis township, which has been his home part of the time since. He preferred the town to the country, hence lived most of the time in Alexandria. During his last sickness he was at the home of his daughter, Mrs. R. L. Jobes, Mrs. Alfred Knutson, and Mrs. Ole Stedge, all residing in this county. The funeral was held Sunday afternoon from his residence in Osakis Township, the remains having been removed from that place. After the services at the house the remains were taken to the Danish Church in Osakis, where services were held, Rev. Markuson officiating. Interment was then made in the Nelson Cemetery. The pallbearers were Hans Jensen, Hans Larson, J.P. Simonson, Rasmus Simonson, Louie Hanson and George Hanson. There was a large attendance at the funeral of Mr. Anderson's old neighbors and friends. Nearly 75 teams followed the remains to the church at Osakis and about 50 teams went from the church to the cemetery.

Danish information from the Danish Family Search website:
1860 census information for Jacob Andersen, including his parish of birth:
Census Year 1860
Name Jacob Andersen
Gender Mand
Age 24
Born Year 1836
Born Placename Karise sogn (parish), Præstø amt (which is south of Copenhagen)
House Role gaardbestyrer (runs a farm).
Marital Status Gift (married
Family No. 5
Matr no. en Gaard
Parish Spjellerup
Hundred Fakse
County Præstø
Placename Spjellerup by
Religion Lutheraner
Original Religion Lutheraner
Record No. 40

Information for his wife in the same census, they have no children yet, so must be recently married.
It may be possible that they are living with Maren Jensen's parents? Jens Pedersen, and Kirsten Olsdatter? Maybe.
38 Jens Pedersen Male 67 1793 Married gaardejer.
39 Kirsten Olsdatter Female 63 1797 Married Hans kone
40 Jacob Andersen Male 24 1836 Married gaardbestyrer.
41 Maren Jensen Female 26 1834 Married, his wife.

Census Year 1860
Name Maren Jensen
Gender Kvinde
Age 26
Born Year 1834
Born Placename Spjellerup sogn (parish), Præstø amt (municipality)
House Role Hans kone (his wife)
Marital Status Gift
Family No. 5
Matr no. en Gaard
Parish Spjellerup
Hundred Fakse
County Præstø
Placename Spjellerup by
Religion Lutheraner
Original Religion Lutheraner
Record No. 41

The 1870 Denmark census shows this couple with two daughters, and the emigrated shortly after the census, according to records in Minnesota.
261 Jacob Andersen Male 33 1837 Married Husfader Gaardfæster
262 Karen Jensen Female 35 1835 Married Husmoder
263 Ane Marie Andersen Female 8 1862 Single Datter
264 Ane Andersen Female 6 1864 Single Datter
265 Inger Kirstine Andersen Female 3 1867 Single Datter
The daughter Ane Marie becomes Marie Andersen in Douglas county, Minnesota.
the daughter Inger Kirstine Andersen, age 3, died shortly after they got to Minnesota, she died in September.

The emigration record for this family leaving Denmark on May 12, 1870.
The Father:
Name: Andersen, Jacob Occupation: Landmand
Age: 33 Destination: Iowa City
Contract no.: 114500 Registration date: 5/12/1870
Last res. parish: Fakse Last res. county: Præstø
Last residence: Faxe, Præstø A. Destination country: USA
Destination city: Iowa City Destination state: Iowa
Name of ship: Indirekte
IDcode: I6971A1817

The Mother:
Name: Andersen, Maren Occupation: Hustru
Age: 35 Destination: Iowa City
Contract no.: 114500 Registration date: 5/12/1870
Last res. parish: Fakse Last res. county: Præstø
Last residence: Faxe, Præstø A. Destination country: USA
Destination city: Iowa City Destination state: Iowa
Name of ship: Indirekte
IDcode: I6971A1818

The three daughters:

Name: Andersen, Ane
Occupation: Barn
Age: 06 Destination: Iowa City
Contract no.: 114500 Registration date: 5/12/1870
Last res. parish: Fakse Last res. county: Præstø
Last residence: Faxe, Præstø A. Destination country: USA
Destination city: Iowa City Destination state: Iowa
Name of ship: Indirekte
IDcode: I6971A1902

Name: Andersen, Stine
Occupation: Barn
Age: 03 Destination: Iowa City
Contract no.: 114500 Registration date: 5/12/1870
Last res. parish: Fakse Last res. county: Præstø
Last residence: Faxe, Præstø A. Destination country: USA
Destination city: Iowa City Destination state: Iowa
Name of ship: Indirekte
IDcode: I6971A1903

Name: Andersen, Marie
Occupation: Barn
Age: 08 Destination: Iowa City
Contract no.: 114500 Registration date: 5/12/1870
Last res. parish: Fakse Last res. county: Præstø
Last residence: Faxe, Præstø A. Destination country: USA
Destination city: Iowa City Destination state: Iowa
Name of ship: Indirekte
IDcode: I6971A1901

Douglas County Album of the Ages, p. 431, published by the Douglas County Historical Society (about 1979)
THE FAMILY OF JACOB AND MAREN ANDERSON
Jacob and Maren Anderson were born and raised in Denmark, Jacob in 1836 and Maren in 1834. They were married and lived in the town of Spellrup near Copenhagen, where Jacob was engaged in the trade of blacksmithing. Three daughters were born, Maria-1862, Anna-1864, Inger-1866.
The family immigrated to America in 1868 and settled in the village of Nelson, Minnesota, county of Douglas, on property now belonging to Erhart Froemming.
Here there young daughter Inger passed away in 1870 at the age of four. She was buried in the family plot in the Nelson Cemetery. In 1876 another daughter was born. She was named Stena and was to become the mother of this writer (Leighton Knudson also buried at Nelson Cemetery).
In 1894 Jacob purchased the "Minnesota House" hotel in Alexandria. This was on of the pioneer hotels in the area and was located on Broadway in Alexandria, Minnesota where the Andria Theatre now stands. (west side of Broadway, midblock, between 6th and 7th Aves.) During this period he also purchased land in Osakis township. on this property he planted trees and constructed buildings including a large brick house which was completed in 1897. He later sold the hotel in Alexandria and moved with his family to this farm home. Here he lived out his life with his wife and two of their daughters, Maria and Stena. Jacob passed away in 1904, Maren in 1915. By this time the farm had become the property of Alfred and Stena Knudson.
The daughters married and continued to live in the Alexandria area.
1. Maria was married to Ole Stedje of Carlos and lived at the farm home with her parents where she ended her days in 1944.
2. Anna was married to Richard L. Jobes (Dick) in 1890 at Alexandria where they spent their entire lives.
(More information on Richard Jobes and wife Anna Andersen on their Findagrave listings)
3. Stena was married to Alfred Knudson (b. 1871), son of Lars and Anna Knudson in 1897.
(more information on Stena and Alfred Knudsen's Findagrave listing)

See additional obituary added as a photo. A note on that obituary sheet says that Jacob Andersen owned the first restaurant in Nelson, Minnesota (near the depot and tracks) called The Blue Goose.