Before I deliver my answer, we must ask ourselves what Sage Mode is.
What is Sage Mode?
From Sage Mode article:
Sage Mode is the empowered state humans enter when they learn to draw natural energy inside them and blending it with their chakra. By doing so, the human creates new senjutsu chakra that allows them to enter Sage Mode.
The next question is: Where do shinobi learn it from?
Thus far, Sage Mode has been shown to be taught in two places: at Mount Myōboku by the toads, and Ryūchi Cave by the snakes.
The articles clearly states that Sage Mode is achieved when the user learns to draw natural energy and mixes it with their chakra, and Mount Myoboku and Ryuchi Cave are two known places where they can learn to do so.
Now, the requirements for learning Sage Mode:
According to Fukasaku, only those who already possess "extreme chakra levels" can utilise natural energy to invoke senjutsu.
Hashirama Senju's Sage Mode
Let us move onto Hashirama Senju.
Because of his large chakra reserves, Hashirama is able to use senjutsu by entering Sage Mode, a feat he could perform instantaneously; it is not known where he learned it.
If we look at his abilities section:
He is similarly knowledgeable of skills he has no training in, being able to recognize the Samsara of Heavenly Life Technique.
Taking into consideration the aforementioned details, in conclusion, it is possible that Hashirama learned Sage Mode by himself. Since it is self-taught, it is not animal-influenced. Hence it would be something-like a "Normal-Without-Animal-Influence-Sage-Mode".
What led me to this conclusion?
Learning Sage Mode at Mount Myōboku or Ryūchi Cave grants the user with a toad and snake-influenced Sage Mode respectively,
That is the explanation for the toad/snake techniques used by Jiraiya/Naruto and Orochimaru/Kabuto.
However, Hashirama's Sage Mode hasn't shown what animal-influence it possesses so far. Therefore, he couldn't have learned his Sage Mode from Mount Myōboku or Ryūchi Cave.
His Sage Mode strengthens his Wood-Release techniques and his overall performance drastically.
From Naruto manga, Chapter 657, Page 08:
Madara-sama's line: "Only this much power... This will be easy to handle.", shows that an experienced and powerful shinobi can use Senjutsu within mere moments.
Since there is no official details about what Sage Mode Hashirama uses, my conclusion is classified as a possibility.
Another possible conclusion is detailed in this answer: Is there a slug based Sage Mode?