As ∞ is not the same type of object as 1, 5, 6 3, etc; the sequence isn't technically well defined. Actually ∞ itself isn't well defined as it could be one of an infinite number of cardinal numbers.
Something along the lines of "1 1 \aleph _{0} 5 6 3 3 3...", with each element being a well-defined cardinal number [1], might be technically closer to being correct, but it is still confusing.
From context all the numbers are cardinal numbers since we are talking about the size of a set (i.e. the set of different regular polytypes in each dimension). Also from context the infinity here must be countable, so indeed it must be the sequence "1, 1, \aleph _{0}, 5, 6, 3, 3, 3...". You don't need to spell everything out explicitly as long as it is clear from the context.
If we want to get really formal, then what we have is a mapping from the natural numbers into equivalence classes of sets under the bijection equivalence relation.
Well, the argument is that for any natural number n we can make an n-gon. So we have a one-to-one correspondence between natural numbers and dimension 2 polytypes, so by definition the cardinality of that set is aleph zero
Something along the lines of "1 1 \aleph _{0} 5 6 3 3 3...", with each element being a well-defined cardinal number [1], might be technically closer to being correct, but it is still confusing.
(Also, sorry for the TeX).
1. https://en.wikipedia.org/wiki/Cardinal_number