Even though this question is a bit old, it's one that I have wondered about for a long time, and so I think it's worth elaborating on the question and the answer. For a long time I thought the "allows to verb" construction was limited to non-native speakers of English. But I've been encountering it so much lately (e.g. here), even sometimes in the writing of people whose grammatical reliability I wouldn't otherwise question, that I've begun to wonder.
@Bill's answer sheds some important light on how rare the questionable construction is, its usage trend over time, and whether it occurs primarily in the language of non-native English speakers. I agree with his conclusions... more on that at the end.
But I think an important point has been left unsaid, and that is that the difference between the forms that sound right (to those writing on this page) and those that don't is not so much the adjacency of the words allows and to, but the presence of a direct object of allows (that is, the subject of the infinitive phrase describing the activity being allowed).
This explains why @Jim's sentence is grammatically correct, though awkward:
It allows to pass certain particles while trapping others.
It's correct in the sense that allows has a direct object (certain particles), even though the DO's placement in the sentence is atypical. I think Bill was alluding to this, but it's worth making the DO aspect explicit.
This also explains the two 19th-century examples that Bill found. The first has a DO in the form of whom, which has been fronted in the pattern of relative clauses. It could be reordered this way to make the DO relationship clearer:
It [the assembly] allows whom [all persions] to be present at its proceedings.
The second 19th-century example is quite different, in that it is not an example of the questionable pattern the OP was asking about:
allows to infinitive verb
Though part of the sentence is not shown, it's clear that the sentence follows one of the alternative patterns:
allows [IO] noun
Here, to him is a prepositional phrase, not an infinitive verb, and expresses the indirect object of allow.
Since this sentence doesn't fit the pattern that the OP was asking about, it doesn't contradict Bill's and the OP's conclusion that "allows to infinitive verb" is ungrammatical.
And that highlights one of the limitations of Google ngrams searches... as valuable as they are, they are limited to looking at surface structures, and the relationship between surface and underlying grammatical structures can be tricky.
It would be interesting to do a similar search in a grammatically-tagged English corpus. Anyone?
Update: results of tagged corpus search
Searching with the query
allows [pos="TO"] [pos="VV"]
where TO indicates an infinitive to and VV stands for the base form of a verb, yields 8 examples out of the BNC. Two of those fit the pattern of the first 19th-century example above: the DO is present as a fronted relative pronoun. Some of the other examples are of generally ungrammatical, unedited oral, and/or technical language, and so might be considered unreliable guides. However, the number of occurrences of this phrase in technical/academic language in the BNC query results and also in the Reuters corpus suggests that the questionable construction is starting to establish a beachhead in accepted English writing of some genres. For example,
- 'The bill allows to incorporate state-owned companies quickly as the first step to their privatisation.' (link) (Actually, I'm not sure whether this is a valid example, since companies might work as the DO of allow / subject of incorporate, instead of as the DO of incorporate. The latter would be more consistent with normal sentence order of course.)
- '"The key element in the Mont Sainte-Odile case is the plane 's abnormal descent rate. Nothing was recorded which allows to say if it was commanded willingly or unwillingly, " he said.' (link)
Of course, these searches are limited too; they would miss, for example, any sentences where an adverb intervened between allow to and the verb. One could also search on the forms allow and allowing, but allowed usually signals a passive construction, in which case the "DO" (now in Subject position) is probably always present but is harder to detect automatically.
In conclusion, I agree with Bill that "allows to verb" is probably a Germanism, indeed probably an importation from many languages in which a construction equivalent to allow doesn't require an explicit subject of the activity being allowed. I tend to read a fair bit of software documentation, and in that kind of writing, since a particular subject (person) is not in focus, it's convenient to be able to leave out the subject (as you can in the sentence "It's convenient to verb.") I imagine this convenience has largely driven the omission of the DO of allow by non-native speakers, and is even starting to tempt the unwary among native speakers. :-)