"Один студент, три студенти, п'ять студентів, п'ятнадцять студентів"
Translation:One student, three students, five students, fifteen students
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I don't think so.
In this case I'm sure 1,3,5 and 15 were chosen not because they belong to the Sierpiński's triangle sequence but more or less randomly just to illustrate some patterns in the word ending (well, these numbers alone won't do the job properly, but in combination with other sentences it can work).
On the other hand, oesis.org is a database of integer sequences.
People came up with so many different sequencing so virtually any combination of 5-6 integers you can come up with will probably belong to some sequence. Try it for yourself - feed the website some integers - whatever you wish, 1,6,78, for example - and there's a chance you'll get some sequence with a fancy name. It won't always work, but if you don't feed it too many mumbers and if they're not too large, you'll probably find them in some sequence.
For my random sequence above it was Diagonal of the rational function of six variables 1/((1 - w - u v - u v w) * (1 - z - x y)) ;)