Syracuse University (College)??
1937-38 Buffalo Bisons (NBL)
Went to Syracuse, allegedly, but I do not see his name on the list of basketball letterman there. Played seven games for Buffalo. That's all I can find.
There was a Stan Jackson who played hockey for Buffalo Bisons in the international league in 1933. He was a former NHL player (1898-1955) and likely is not the basketball player.
One source identifies Jackson as Stanley J. Jackson (April 9 1920 - November 1981). However, this would make him 17 when he played with the Bisons, which is highly unlikely.
One other possibility I saw: Stanley John Jackson. Born in 1913, he graduated from U of Buffalo in 1937, died in 2001 after long career as a doctor. Has a son Kenneth who lived in Fairport, NY.
I could not find the middle name of the 1920-1981 Stan Jackson, nor do I know where that source got the player's middle initial, but if the initial is accurate but the identification is not, it very well could be Dr. Stanley Jackson, 1913-2001.