Is there a word like cardinal or ordinal but for the “single, double, triple” series?
The words one, two, three, and so on are the cardinal numbers.
Similarly, first, second, third, and so on are the ordinal numbers.
Is there a similar term for the words single, double, triple, and all the rest?
These are called multiplicatives by Fowler (1850). The term multiplicative is also seen to describe the words once, twice, thrice, and it seems reasonable to distinguish the former as multiplicative adjectives, and the latter as multiplicative adverbs.