  In this paper, we give a type B analogue of the 1/k-Eulerian polynomials.
Properties of this kind of polynomials, including combinatorial
interpretations, recurrence relations and gamma-positivity are studied. In
particular, we show that the 1/k-Eulerian polynomials of type B are
gamma-positive when $k>0$. Moreover, we obtain the corresponding results for
derangements of type B. We show that a type B 1/k-derangement polynomials
$d_n^B(x;k)$ are bi-gamma-positive when $k\geq 1/2$. In particular, we get a
symmetric decomposition of $d_n^B(x;1/2)$ in terms of the classical derangement
polynomials.
