[seqfan] Dirichlet eta function and Stirling Permutations

[Mario Krenn]

The sequence A156919 <https://oeis.org/A156919> apparently indicates a 
connection between Stirling permutations and the Dirichlet η-function: 
"Stirling permutations were discovered while studying certain properties 
of the Dirichlet eta function."

Unfortunately, there is no further explanation of that connection, and 
literature search didn't lead to any result.
I have asked that question also at mathoverflow, where there is no 
answere yet: 
https://mathoverflow.net/questions/308107/dirichlet-eta-function-and-stirling-permutations

I would very much like to understand in which context the Stirling 
permutation arise in the study of the Dirichlet eta function. Every hint 
or reference to the literature is very much apprechiated.

Thank you,
Mario