  In the present investigation, we consider a subclass of starlike functions
associated with a petal shaped domain, recently introduced and defined by
$$\mathcal{S}^{*}_{\rho}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\sinh^{-1}
z\}.$$ We establish certain coefficient related problems such as sharp first
five coefficient bounds along with sharp second and third order Hankel
determinants for $\mathcal{S}^{*}_{\rho}$. Also, sixth and seventh coefficient
bounds are estimated to obtain the fourth Hankel determinant bound for the same
class.
