There seems to be a problem.
There seems a problem.
In this type of construction, the version with to be, such as (1), is much more productive than the one without, such as (2). See this Ngram: There seems to be a,There seems a
There seems to be little doubt that....
There seems little doubt that....
In this similar construction with "little", however, the version with to be, such as (3), is even less productive than the one without, such as (4). See this Ngram: There seems little,There seems to be little
Would there be any logical explanation of this apparently counter-intuitive usage data?