This is my original posting which seems to be based on erroneous information: He appears from the burial records of Early Settlers of New York State by Janet Wethy Foley to have been a son of Col. Henry Livingston Van Rensselaer. Jacob Rutsen Van Rensselaer died at the age of 68 years and 21 days according to Foley.
On May 9, 2014, I got an email message from a Find-A-Grave contributor LEIGH that based on the baptismal records of the Dutch Reformed Church of Claverack, Columbia County, New York that LEIGH believes that the parents of Jacob Van Rensselaer were Robert Van Rensselaer and Cornelia Rutsen (daughter of Jacob Rutsen and Alida Livingston).
THE NEW INFORMATION FROM THE SECOND PARAGRAPH IS CORRECT.
Also, I just found a Wikipedia entry for the Jacob Rutsen Van Rensselaer House and Mill Complex at Claverack, Columbia County, New York. It says that the complex was started about 1805 and consists of 14 interrelated buildings and is on the National Register of Historic Places since 1982. The main building seems to be a two story brick house with an English basement built about 1805 with a two story addition added in 1929. There is also an Italianate dwelling in the complex that is worth mentioning.
Cornelia De Peyster Van Rensselaer
John R. Van Rensselaer
Jeremiah Van Rensselaer
Alida Van Rensselaer Kane
Henry R Van Rensselaer
Catharine Van Rensselaer Schuyler
Angelica van Rensselaer How
James Van Rensselaer