Eulerian polynomials, perfect matchings and Stirling permutations of the   second kind
  In this paper, we first present combinatorial proofs of a kind of expansions of the Eulerian polynomials of types A and B, and then we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the second kind by their cycle ascent plateaus, fixed points and cycles. 
Shi-Mei Ma, Yeong-Nan Yeh
math.CO